I have killed a few deer with the 243 but I am not a fan of it for big game. I have a 6.5x55 on a Mod 70 featherweight and it's about perfect, if you hand load. If ya don't, I'd take a look at the 260 Rem. Only draw back on it may be finding ammo. For some reason it didn't take off like I hoped it would. I've never shot a 7-08 but have had several 7x57's. What I hear the 7-08 is easy on the recoil. Must be as it's a bit smaller than the 7x57 and that is great to shoot.
Another that is fairly easy shooting is the 308 Win. I've had two and have killed a lot of deer with them and a few elk.