I would go with the .243, and the .223 would be my next choice. The .243 is really nice because it can honestly be a great varmint gun, and a great whitetail deer/pronghorn cartridge. It is very light on the shoulder which makes it extremely fun to take to the range and have fun with. There are a ton of bullet options out there for the handloader. It is a relatively cheap cartridge to reload, powder capacity is not a whole lot and since bullets are small, they tend to be fairly inexpensive. It is a really popular cartridge too so if for some reason you decided to stop handloading, there still would be a lot of factory loadings available at most sporting goods stores.
The .270 is pretty close to the .308 as far as power level goes. You would use it to hunt the same animals really and wouldn't gain you much of anything. As a matter of fact, it might be more expensive to reload slightly due to its increased case capacity. It is a smaller diameter bullet going faster, so you gain a flatter trajectory but your energy levels aren't that much different.
I think the .243 is a great choice for you, I recently added one to my collection.