Ditto everything on froggy. You should fishless cycle, but if you already have the fish, you'll need to change the water daily to keep ammonia out, and other stuff that builds up, that you will be reading about in cycling.
as far as size, the benefits of having a 29g as opposed to a 5 also include a more stable environment. If there are toxins in the water, you have a longer time before they are deadly. temperature shifts less. if you run into problems, like over feeding, a larger tank can be more forgiving until you figure your problems out. Plus you can have a lot of cooler stuff. The set up new would probalby be in the ball park of 200$ (tank, hood, stand, lights, heater, filter) and you can use your 5 as a hospital tank or q-tank (quarentine for new arrivals, so it wouldn't go to waste.)
if you keep the 5g, a betta is good, I don't know about cories, I think they need schools and prefer more swiming room. Mine do at least. You can also do the water change option with the betta (and African dwarf froga - not the clawed ones!), changing the water instead of cycling.
www.bettatalk.com and
www.bettaforums.com should have info on that. If your tap is not from a well, you may need water conditioner, if you haven't found that in your research.
Good luck!! sounds like a great family project!