Fancy goldfish can grow up to 8", common goldfish can grow much larger. What type he is will dictate what tank size will be appropriate. I would make the goldfish your priority. They are very dirty. I don't have experience with goldfish and snails, but a quick search says it's not a great idea. That's what I've found, but maybe our more goldfish-savvy members can help there.
With the betta, I'm not familiar with any betta cube larger than 2.5 gal? Many people say a 5 gal. is a good minimum size for bettas. But like I said, IMO the goldfish is the priority right now. If you could get your hands on a heater and filter for the betta that will be good enough for now. Bettas will sometimes eat snails; It depends on the betta.
Do you have a test kit? If you don't, API Freshwater Master Test Kit is highly recommended. It's actually more economical than test strips in the long run, and is much more accurate.
Good luck and welcome to AA.