Another slug gun hater here. No hyperbole, I'd much rather shoot my .338 Win Mag than my 870 slugger (well named). It has everything to do with the stock.
For the OP, don't be buffaloed by recoil. If you want to shoot a .308, you will, and you'll enjoy yourself. Get one of those gel pads that fit inside your shirt if the recoil pad on the gun is too stiff. However, if you don't care whether it's a .308 or a .243, then you won't have the motivation and your initial (and natural) aversion to being thumped will put you off it for good. Are you motivated?
Someone mentioned 6.5 mm bullets. I'm a big fan, and the 6.5's have proved themselves in long range shooting. The 6.5 based on the .308 case is, of course, the .260. That might be a better choice, and not only for the reduced recoil.