I see that you are from Alabama. Are you going to hunt there?
The reason I ask is that usually, in the Southeast, ranges don't tend to be all that long, nothing much over 200 yards.
If that is the case, a lever action .30-30 will do what needs done just fine. And you can get a new one in your price range, no problem. For instance, you should have no problem finding a new Marlin 336W for considerably less than $400. Look around and you can find a used Marlin 336 for less than that. Throw in a set of Williams peep sights, or scope it if you wish, you'll still be well within your budget.
For instance: A few years back I bought my NIB 336A (similar to the W model except for the front stock configuration) for $299 on sale at the local Dick's Black Friday (after Thanksgiving) Sale. I added on a Leupold VX-I 2-7x33 scope ($179, on sale at Amazon believe it or not) and a set of Leopold low profile QRW rings that were just over $50, IIRC. The rifle came with a Weaver 63B scope mount, but those are cheap anyway. Anyway, the whole she-bang ran just over $500 + tax. Nice hunting setup on the cheap.
Looking at your budget, I have to ask if is that figure for the rifle, the shotgun, or is that a total figure for both?