I own a .243Win, .25-06, and a .280AI. None of them really have that much recoil in my opinion. The .280Rem will have the most when using heavy bullets but it is still not bad.
I have killed large western Mule deer and an Elk with both the .243Win and .25-06 and none of them required second shots. The 7mm-08 is another great cartridge that would do well on deer or larger game.
As far as the Rifle's are concerned Tikka makes a nice rifle but the only bad thing about them in a .243 is they use a 1:10" twist so the 100gr bullets might not work as well. All the other calibers the twist rates are about right for caliber. Ruger makes a nice rifle as well as others. The TC Venture just had a recall notice so that might be a concern for me. CZ makes a very nice rifle as well. Try and hold as many rifles as you can and make sure they fit you both well before you purchase one. A properly fitted rifle will certainly help with recoil. And if you do find recoil to be a problem then you can always install a limbsaver recoil reducer buttpad that will help reduce any felt recoil.