Ultimately, the best rifle and cartridge is one you can shoot accurately. For ranges under 200 yards, the .30-30 Winchester is the time tested deer slayer. Beyond 200, .25-06, .308, .30-06, and .270 are good. For very long range (400+), try any of the .26 through .30 caliber magnums. The truth is, any centerfire cartridge from .243 on up will kill deer well if the bullet is placed properly. For hunting in dense cover, lever, semi-auto, and pump action rifles are popular because they allow quick follow up shots. Bolt actions are often used in more open country and the overwhelming favorite in the western U.S.
If I had had the money, I'd go with a European double rifle in 6.5 x 55mm Swedish or a Browning BLR lever gun in .308. If I had a limited budget, I'd get a Savage in .308 Winchester and never look back. That said, the scope is perhaps more important than the rifle, so spend your money there.