A ten-gallon tank is a useful size for raising livebearer fry. While you need a heater, lighting isn't required, and for filtration you can get by with a very basic system. I use a 'box filter' and an air pump. Don't use an undergravel filter or anything difficult to clean; with fry, you want to keep the tank as clean as possible. This isn't so much an issue with livebearer fry, but withy egg layers (like cichlids) it's very important.
With few exceptions, fish are best raised _away_ from their parents. The exceptions are things like discus and orange chromides, where the parents provide food for the babies. But more generally, adult fish simply view baby fish as food. In the wild, this doesn't happen because the parents and the babies will live in different places. So for guppies, the fry will immediately swim into floating plants or very shallow water, where the parents won't go.
Having a small breeding tank is one of the most useful investments an aquarist can make. Besides raising fry, it can be used for quarantining new fish, for treating sick fish, or for use as a refuge for fish that need rest and fattening up (e.g., females after spawning/breeding). Use water from the main aquarium to speed up the maturation.
Cheers,
Neale
PS: I have a
'breeding diary' about my halfbeaks, also livebearers, on my web pages. You might find some of that interesting; it will give you some information on the types of food you can use, how quickly fish grow, and so on.