RE: .308 or 30-06
In a lever action I would go with the 308. It is a shorter cartridge and will probably cycle better, in addition lever guns are not known for their accuracyand the 308 has more than enough power out past 300 yards for deer. This is probably as far you will be accurately able to shoot a lever action anyway given the size of a deers vitals. Also many lever action guns have shorter barrels which are better with the 308 due to its smaller case capacity. It is kind of expensive but take a look at the browning lever it uses a rotating bolt to seat the cartridge similar to a bolt action.