I think first off you want to check out the pinned topics in this forum and the one on rarer livebearers.
Some people like the colours and playfulness of the standard species (platies, guppies, etc.) while others prefer the less commonly seen species (halfbeaks and goodeids, primarily). I happen to like halfbeaks, but they're not for everyone, and probably not ideal beginners fish since they can be delicate. Goodeids, mind, are generally quite tough.
You also need to think about space. Adult sailfin mollies are around 10 cm long, and the giant sailfins are even bigger, up to 15 cm long. So these are cichlid-sized fish that need plenty of room, and when kept in small quarters get stunted and never grow their sail fins to full size. Endler guppies, on the other hand, are tiny, with the males around 1.5 cm and the females only a bit bigger.
Water conditions are an issue too. Halfbeaks will be fine in soft water, while most of the standard livebearers as well as most goodeids need hard, alkaline water. Mollies and the infamous (but very impressive) pike livebearer need brackish water.
If you're serious about breeding, then it's best to pick a target and concentrate on getting the best quality offspring. Different varieties of guppy, for example, will all interbreed, so if you want to concentrate on (say) green cobra guppies, then you may want to spend a little more to get good, virginal stock to start your colony with. If you want a challenge, then breeding giant sailfin mollies and Celebes halfbeaks are both tricky enough to need some care, but easy enough that you'll get results. With the giant sailfins, it isn't getting babies that's the problem, but raising males to their full 10 cm size with almost as large sail fins.
Basically, livebearers have something for everyone, and you'll find them a lot of fun as well as being an especially interesting group of fish.
Cheers,
Neale
