Almost everyone who has them, breeds them, and not always by personal choice.
Livebearers are very easy to breed, basically stick a male with 2-3 females and you will have babies. I suggest you read all the pinned topics, and the ones in the FAQ, as they should just about answer all your questions. Don't expect to make much, if any money from this. The common Livebearers (Which are most likely the ones you are able to get) are very common, since they breed easily. Most fish stores will take fry for just a little amount of money, and you have to spend the time and money to get them to a decent size to sell. This isn't the thing to go into for money, unless you are doing it on a very large scale. If you just want to do it for fun, make sure you
do have a pet store that will take the babies, as not all will.
Other fish include Endlers, Mosquito Fish, Halfbeaks, Goodeids, and Four-eyed fish, amoung others.
Breeding is very easy, as I mentioned above. Tank size would depend on what Livebearer you'd like to breed, but usually about 15-30g is good for the adults. Fry tank size is usually about 5-20g. Feeding and other things like that are in the pinned/FAQ topics.
My own personal experience isn't much for breeding, the fish bred for me. I mostly know about fry coloring/genetics, raising and size in relation to foods, and just general complex fry stuff no one wants to know about.

I do have a few pointers though...
- Always make sure you have the ratio right, with the common Livebearers.
- Feed the pregnant females good, high-protein foods before and after birth, to help with their strength. It's also good to continue feeding this throughout their life, just because it helps balance their diet, but it's especially good around labor.
- Don't put them in a breeder net or trap. They can work, but they also run the risk of highly stressing them out. It's best to let them give birth in the tank, or in a fry tank.
- Feed the fry 4-6 times per day
- Alternate the fry's food. Veggies, high-protein foods (Such as small frozen, freeze-dried and live BBS) and flakes work. When they are young, just fry food is a pretty balanced diet for them.
- Be patient! Fry take a while to grow, and the mother takes a while to have birth.
- And last but not least, have fun!