The lower receiver will limit your caliber choice. You can get an AR-15, or you can get an AR-10. Then there are some other variations that are not universal (i.e. parts only available from one source) that will give you a few other options. The AR-15 can be chambered in 5.56NATO, 6.5 Gredel, 6.8 SPC for a start. The AR-10 can be chambered in .243 Winchester, .308 Winchester for a start. .308 is most common for AR-10s, and .223 is most common for AR-15s. The magazine well is the biggest limiting factor that determines this - also keep in mind that magazines are a lot more expensive and harder to find for the weirder/newer/better/etc calibers.
Sounds like a good plan! The only thing I would change would be to buy 10 magazines and a case of ammo every time, instead of "some" ammo and "a" magazine. Happy shooting!