I am rasing my second baby betta from petco, and since they are soo small at first i use a .5 gal critter keeper with a marimo betta heater and a hand full of plants, i change the water every night, and feed as much as i can 3-4 times a day. I use a mixture of freeze dryed food and Aqueon betta pellets crushed up into size it can eat, and gradually increase the size. I also feed frozen brine shrimp once right before water change.
I make sure to monitor the water temp, and I move the baby up in tank size as it grows.
I also have soem pond snail in with it, since i keep the tank pretty green, as in algae. I cup the baby with the cup it came in and float it every water change, I also only rinse the tank with the old water, then add fresh.
I posted a pic on my set up on another thread but here it is again so you can see.