What follows comes from just one fishkeeper's experience (mine), and in no way do I claim this to be a definitive list. Probably no two aquarists' lists of great beginner fishes would be the same. There are so many choices! My list comes from what I've learned during more than 40 years of keeping tropical fish. I'm sure at least some of you will disagree with me. Not a problem - it's a big hobby.

What I'm going to propose are different groups of fish that are good beginning choices. Each group has a number of individual species or color varieties in it.

Criteria
Let's look first as what we mean by good beginning fish. There are a number of factors by which a fish can qualify for inclusion in this select list of finned friends.

Hardy
The first qualification for a fish to be a good beginner's species is that it must be very hardy. The fish must be able to put up with less-than-perfect living conditions (a little overfeeding, sometimes a lack of feeding, infrequent water changes, some overcrowding and so on). This doesn't mean I condone improper fish care. I'm just being realistic, and the fact is that folks starting out in the hobby may not always provide their fish ideal living conditions. Beginner fish need to be able to take this kind of treatment and survive.

Peaceful
To qualify for inclusion here, a fish must be peaceful - not only toward other fish species but its own, as well. Put simply, fish that are highly territorial (with two exceptions mentioned later) or just plain nasty and tend to pick on or actually do battle with other fish are not acceptable. We want everyone to get along.

Easy to Feed
Beginner fish must be able to thrive (not just get by) with a diet completely composed of dry, prepared fish foods. There are many excellent brands of prepared food on the market, with a wide variety of formulations. In addition, there are many other packaged "treats," such as freeze-dried brine shrimp, bloodworms and mosquito larvae. All of these provide a complete diet for most fish, but you still should feed a variety of the dry foods. This does not mean that you should refrain from feeding frozen or live foods, but these fish don't need anything but prepared dry foods to do well.

Attractive
Now, we start really getting into opinions. The phrase "beauty is in the eye of the beholder" never applied more than to tropical fish. I've included fish I think are attractive.

Commercially Raised
One nice thing about the tropical fish hobby is you can enjoy it and find plenty of fish to choose from even if you limit yourself to those that have been raised commercially for the ornamental fish hobby. I'm not saying we should not keep fish that are caught wild, but there are so many species raised commercially there's really no need to look further. Captive-raised fish are usually healthier and less stressed from capture and shipping, and buying them preserves wild populations, as well.

Working With Your Water
Keep fish that will do well in your tap water. Without getting into a discussion of the specifics of water chemistry, let's briefly consider two things: pH and hardness. The pH is the measure of the acid/alkaline balance of water. Hardness is the measure of the dissolved solids in the water.

Water pretty much splits into two types: soft/acidic and hard/alkaline. You can bring a sample of your water to many local fish stores, and they will test it for you. Better yet, you can buy inexpensive test kits for pH and hardness, so you can monitor water conditions as they change in your tank.

Particularly when starting out in the hobby, it is much easier and you will have more success if you keep fish that prefer your water conditions. Trying to make hard/alkaline water into soft/acidic water is difficult and somewhat expensive. Making soft/acidic water into hard/alkaline water is a bit easier because you are adding elements to the water, not trying to remove them. Nonetheless, this is still something you should not deal with when beginning in the hobby. In addition to pH and hardness, we also have to consider whether we want to heat the tank for the fish or just leave it as a coolwater tank without a heater.

The Fish
I'm going to divide the groups of good beginner fish into the following groupings: two for unheated tanks with average hardness and neutral pH, four tropical species for soft/acidic water and four tropicals for hard/alkaline water.

Unheated tanks

Danios
Danios are a family of fish, the most common of which are zebra danios, pearl danios and giant danios. There are numerous variations with long, flowing fins and different colors and/or patterns. Danios do best in a long tank, such as a 20 long, because they are actively swimming all the time, and they like plenty of room to swim the length of the tank before needing to turn around. They are schooling fish, so the more the merrier - you should have at least eight or 10 of each type to keep them at their best. All of the danios are prolific breeders and therefore are very inexpensive.

One very interesting fish that's just now entering the hobby is a "phosphorescent" zebra danio. A gene for phosphorescence is "planted" into the DNA of a zebra danio, and the fish is reported to glow under the right conditions. Unlike the painted and dyed fish that are available in the hobby, this process does not harm the fish. They are also supposed to be sterile, so prices may be high for quite a while.

Soft/Acidic water

Angelfish
Besides being my favorite fish, angelfish are great beginner fish. They come in many different varieties of markings and finnage and are very easy to keep. Although they can be acclimated to, and even bred in, water that is not soft and acidic, they do best at a pH in the low 6 range, and the softer the water, the better.
Remember that angelfish are cichlids, and therefore will become territorial when they mature, especially when they start to breed. When they reach adult size, if there are any small fish like cardinal or neon tetras, the angels may decide to supplement their diet with some protein-on-the-fin, in the form of any small fish they can consume. And yet, they are beautiful and easy to keep.

Dwarf Gouramis
This is an instance in which the fish breeders of the Far East have taken a fish that was already great and made it even better (at least to some). Starting with two kinds of gouramis, the regular dwarf gourami (Colisa lalia) and the honey dwarf gourami (Trichogaster [Colisa] chuna), breeders have produced some lovely color varieties. They also can manipulate the development of a spawn so that they get only male fish, which are much more colorful than the females.

Regular dwarf gouramis come in a few varieties of solid red and solid blue. The honey dwarf comes in a "red flame," "sunset" and a beautiful golden variety. Any of the dwarf gouramis make excellent beginner fish for soft/acidic water. However, remember that most of what you see in the stores will be males, so if you want to attempt breeding them, you may have to ask the store to bring some females in especially for you.

Neon Tetras
Neon tetras originally came from the Amazon basin, and they prefer soft/ acidic water. In the Far East, primarily Hong Kong, neons are produced by the millions. Buy the large ones (about three-fourth inch), and buy them in schools of no less than eight or 10. Neons look best on darker (even black) gravel and really thrive in a densely planted tank.

A word of warning: In most stores, you will also see cardinal tetras. They look just like the neon, but the red line on the bottom extends from front to back (in neons, the red line is not as long). Cardinals can be difficult to keep, so do not be tempted - as a beginner - to select them over the neon.

Cory Cats
Every tank that has soft/acidic water should have at least one shoal of five to six cory cats (catfish in the genus Corydoras). Many cory cats are produced by fish farmers, and the most common ones that you can rely on being farmed are the albinos (Corydoras aeneas and C. paleatus). Other common species that do come from the wild include varieties of C. melanistius and C. punctatus. They are plentiful in the wild and easy to keep.

Hard/Alkaline water

Livebearers
The best group of fish to start with that like hard/alkaline water are the livebearers. The easiest ones to keep are the platies and swordtails, both of which come in a breathtaking array of colors and finnage. A second group of livebearers that can be a little more difficult to keep are the mollies and the guppies, which are also available in many varieties. If you have success with platies and swordtails and want more challenging fish, you may want to consider mollies or guppies.

Livebearers do best with a little salt added to their hard/alkaline water (say, a tablespoon per 5 gallons). They should also have a lot of vegetable matter in their diet. Feed them some green flakes (Spirulina algae flakes are the best).
As their name says, all these fish give birth to broods of live baby fish, usually about once every 30 days or so. You can save many of the babies if you have floating plants in the tank for them to hide in. You can then move the babies to a tank of their own. In addition to being easy to keep, livebearers are the best beginning fish to get to breed.

Plecostomus
Most fish of the genus Plecostomus (suckermouth catfish also known as "plecos") you will see in fish stores for about $5 have been bred and raised in Florida in hard/alkaline water. They'll do great in a tank with livebearers, Mbuna or Tanganyikan dwarf cichlids (the last two groups of fish we will be covering).
Make sure there is a cave or similar hiding area for each pleco to call its own; they feel most secure that way. In addition to ease of keeping, the other great reason to have plecos is that they eat algae and will keep your tank glass fairly clean. Sometimes, they will also eat soft-leaved plants, but if you feed them some Spirulina disks or pellets after turning off the lights, they will appreciate it (plecos feed mostly at night).

Mbuna: Lake Malawi Cichlids
"Mbuna" is the local native name given to a whole group of many species of rock-dwelling cichlids that come from Lake Malawi in Africa. There are many varieties, and because they breed prolifically, they are inexpensive. Almost any fish store will have at least one tank of "assorted African cichlids." The harder and more alkaline the water, the better, and most folks who keep mbuna use  marine gravel for the bottom of the tank or in a canister filter to keep the pH in the high-7/low-8 range.

These fish are highly territorial (an exception to our criteria), especially as they mature and pair off to breed. This territoriality is easy to deal with by either giving the fish plenty of rocks to hide in and mark territories, or keeping them so crowded that no single fish can define a territory. I strongly recommend you use the first strategy. The alternative strategy works, but requires very heavy filtration and massive water changes. Finally, for mbuna, the bigger the tank the better, and I would consider 30 gallons the minimum size to start with.

Tanganyikan Dwarf Cichlids
From another East African rift lake, Lake Tanganyika, we have a group of dwarf cichlids of the genera Neolamprologus and Julidochromis that will absolutely thrive for beginners with hard/alkaline water. These fish will do best with a pH as high as 8.5 and extremely high hardness. All these fish will breed quite readily in a small tank of 10 or 15 gallons. It's great fun to set up a 15-gallon tank with rocks, coral gravel and caves.

Start with six or eight of the same fish (my favorites are N. brichardi and J. marlieri). Within eight to 10 months, fish in the group will pair off and get ready for breeding. You will know which fish are not the pair because they will be cowering in a corner at the top of the tank or pinned in a corner. Remove these fish - or else the pair will kill them - and the pair will claim the entire tank for their breeding territory. The brichardi will eventually set up a breeding colony with a dominant male, one or more females and the young babies from various spawns all hanging around a breeding cave. It's a wonderful sight.

Alternatively, you can keep a larger tank (40 or 55 gallons) with two or three different species of Tanganyikan dwarf cichlids. As they mature, each species will claim a part of the tank as their own territory. They are easy to keep and easy to get to breed.

Conclusion
There are many different fish to choose from for the beginning hobbyist. It's important that you know as much as possible about any fish you buy, so please read books and subscribe to magazines about fish. I strongly recommend you start with the fish in this article. Also, make sure you select fish best suited to your water conditions.

Above all else, please remember that local fish stores are a great source for advice, and should have the right products for your experience level and (most of all) good healthy fish for your tank. Start off right, and your chances of success are greatest. Good luck in keeping fish - the best hobby of them all.