30-30 drops 7.5 inches at 200 yards, sighted in at 100. Drops 24 inches at 300 yards.
.308, .30-06...maybe an inch or two..still minute of deer. Out here in farm country, see more deer in the early A.M. coming out of the woods...and there is no cover on pasture or cropped field land...so distances are more often beyond 150 yards.
GOOD deer hunters sit in a tree stand and wait for the deer to come to them, so shots are closer. (I hate sitting in the morning cold.)
For $500, around here...you can get a used single shot .22, a used single shot 12 ga., AND a used .308 or 30-06, which are pretty much the same, ballistically.
Mil-surplus rifles...7.62x54 Mosin 44, or 91-30...same size slug, similar ballistics. Enfield? .303...same size, pretty much, slug, and ballistics.
Least expensive on the market today is the Mosin Nagant...up to $150...beyond that is over-priced. Most need cleaning of storage grease, but never saw much use..many made at the end of the war years.
But, until they made rifles ok to shoot around here, I got deer almost every year with a 12 ga. shotgun and a slug, under 100 yards.
read, learn, decide. You can practice in the basement with an air-rifle. At most indoor ranges with a .22. Usually need a range to work with the centerfire rifles.