While I don't support them selling baby fish as that is really hard on the fish. You have the fish now and at least it's not in a small store cup anymore. We can all start a petition against petshops selling baby fish later. For now, congratulations on your new fish! I think this site can provide you with good advice, they just also want to make sure you understand the difference between a good pet to have, and a pet the store should not be selling- I think you understand that, but again you already have the fish so...
I agree with live food, if you can get it and the source you get it from is good enough that you do not have to worry about parasites. Also, try: http://www.petsmart.com/product/inde...ductId=3295905
These are flakes and a breeder i know said he crushes them up and gives them to fry (really young bettas). They are pretty good quality from what I've heard. This will allow you to give the betta more variety.
Can you heat the tank you have him in? You need to be REALLY careful with small tanks as the heaters available can overheat the water and cook your fish. What is in the bigger tank? Is it possible to float the small tank in the bigger tank (so the watter in the small tank will be warm)? I think 80 degreed F is good for a baby betta, but someone else will know more. I just know adults are happy at 76ish and babies need it to be warmer. (Not too hot though. You'll hurt the fish. 85 is the limit, I think...)
You could also get a pre-filter sponge: http://www.petsmart.com/product/inde...ductId=3650250
I have one and it'll keep the baby from getting hurt by the filter. You can also try the methods mentioned on this site to baffle the water coming out of the filter.
Next, get this: http://www.petsmart.com/product/inde...uctId=11147371
It will give you a better heads up on when to change the water. You'll need to be really careful, attentive, and watchful.
It's a baby, after all. Good luck and report back to us as frequently as you can, please.
Now, as mentioned earlier: http://www.change.org/petitions/petc...ng-baby-bettas