I'm not sure what the poultry market is like in AL but I certainly wouldn't worry too much about 're-homing' your extras at 4 months old. If they are production breeds especially (those whose main purpose is to lay eggs, i.e. large fowl, not bantams) the pullets (females under a year old) would be very desirable. They begin egg laying on average at 24-30 weeks, and you and your child would have done the more difficult work of raising the babies, heatlamps, brooder, etc...at 4 months they are pretty much ready to go and will start laying in the next couple of months. You should be able to sell them without trouble (of course that all depends again, on what breeds,etc...and what the going rate is for pullets at "point of lay"). If you end up with some cockerals (young roosters), you'd most likely have to give them away...
Re. coops--since you would only be keeping five hens (unless the infamous chicken math kicks in and you all get hooked!) you certainly would not need a huge coop. The chickens don't care where they live, you simply need a safe environment for them with fresh water and food. I would investigate a way to make a temporary, larger area (estimate about 4 square feet per bird) about 8'x10' maybe using free pallets or the corner of a garage with a secure run outside, then invest your time and funds in a more permanent structure for the ones you keep. Economical is one thing...flimsy and unsafe is another. And make sure you don't use 'chicken wire' with the idea it will protect the chickens. The only thing chicken wire keeps fenced are the chickens--any predator can tear it down, bite through it,etc...best used for dividing inside a coop or something like that.
That sounds like a pretty cool project though--my dd has been involved for over five years now with chicken projects, both production and meat birds--wonderful learning experience and the 4-H books are invaluable, along with BYC of course! Good luck!