If money is a major concern you might want to consider a good used gun. If whitetail is the largest game you'll hunt, then perhaps downsizing the cartridge would be reasonable. Shooting an '06 can, under your limitations, be unnecessary in cost, weight and recoil. The .308 Winchester will do a more than adequate job. The 7mm-08 Rem. is also an excellent cartridge. If you're not limiting yourself to a bolt action, the Savage M-99 is a fine lever action rifle. It came in the .308 Win. and the .300 Savage. The .300 Sav. was about half way between the .30-30 Win. and the .308 Win. While it was a lever action, it was a strong action and did not use the tubular magazine. I'd suggest that you try to find one with a rotary magazine. This magazine was excellent and every round was in line with the chamber for feeding. This rifle has been discontinued but is not uncommon in good condition in gun stores, or even hock shops. Newspaper ads may also be a source. The last models of this rifle were equipped with a detachable box magazine. Personally I prefer the rotary magazine. I hope that this is of some help. Good luck.
BigBob