Well, you are quite right to anticipate a lot of fry ! In general livebearers will eat their young if hungry enough. So the trick is to ensure that the adults are well fed. I colony breed my livebearers, ie mix adults and fry in the same tank. Whether I have Limia, Poecilia, Phallichthys, Heterandria, or Girardinus (these are all livebearers) I have a species only tank. I use a lot of floating plants and java moss, along with hygro to add dense cover. Other livebearer breeders that I know use various plastic plants or plastic type plants that you can get from the dollar store. Thick cover is the key. When an adult is looking to chase, the fry dart into a hiding spot and the pursuit ends. As more fry grow, the adults get used to having small fish around them and then ignore them altogether. When I do not have fry in the tanks, I usually lose the first few babies until enough small fry appear.
Yes, you can also net out the babies and put them in a floating breeder or net cage. That works as well. How long you keep them in there is dependent upon the mouth size of your other livebearers. You have platies and swordtails as well. These are larger fish, so make sure your fry are a few weeks old (size wise). What to feed them ? I feed live food, and small crushed flakes. Depending on the species of fish, I use brine shrimp flakes for insect eating fish and spirolina flakes for vegetation eaters. You can crush flake food into fairly small pieces. Most of my livebearer fry are large enough to take them when a few days old. You can also try the golden pearls, but they are more expensive. Best of luck on the fry