RE: small gun bigger than .243
The .270 would be another great choice as well. Super cartridge and light recoil. I have an eleven year old son and he can shoot my .270 all day long so you should be fine with any of the above mentioned cartridges.
One thing about the .270 and 30-06 is that they are chambered in about 90% or better of rifles made so you will have unlimited choices of rifles to choose from and ammo is everywhere you look. Recoil of these cartridges really isn't that bad at all. You should be just fine with anything up to and including the 30-06.
If you have any friends or relatives that have any guns larger than the .243 then get together with them and go to the range and see for yourself. You just may surprise yourself as to what you can handle.
Good luck with your new rifle when you get it.