alright your calibers of choice are
30-30(generally the cheapest rifles with the best ballistics for medium game)
45-70(big bore, big game getter, stiff kick, fun as heck)
357 mag(good for deer but not really suited to anything past 100 yards)
44 mag(good for deer and smaller predators such as cougar, wolf, and black bear, also restricted by range)
45 colt(kindof in the middle of 357 and 44)
35 remington(no personal experience with this one)
32 special(hard to find, generally expensive but great for anything smaller than elk)
I own a pre-Cerberus Marlin 1894 in 44 mag that is rapidly becoming my favorite rifle to shoot. it is the only lever in my collection
my brother-in-law owned one in 32 special that was also a neat rifle but appraised at double your budget
he now owns a post-Cerberus Marlin 1895 in 45-70 and since he reloads all of his own ammo it is the most versatile rifle I've ever seen.
he has bird shot loads
round ball loads at pistol velocities
shoulder crushing hard cast 416 grain bullets
and my favorite are his "bucking balls": roundball backed with bird shot. low recoil, low volume, surprisingly good penetration and decent birdshot patterns...I kindof want a few for the 44 for home defense loads