I don't hear self defense being a high priority, so I would question the semi-automtic aspect as well. I would echo a bolt .308 or even a lever .30-30 such as a used Marlin 336, though I wouldn't call the latter a "moose" rifle/cartridge either except up close with "shot placement" as usual. The .30-30's certainly done it; it's just not what I'd choose as either a precision target rifle or dedicated "moose" (elk) gun.
The .30-30 and x39 (AK, SKS etc) cartridges are dimensionlly similar, almost to extent one has been called the flat nosed or spitzer version, respectively, of the other. Not exactly so. While the spitzer point of the x39 may suggest "better" long (mid) range ballistics, the .30-30 bests it as a hunter with bullet weight--by. a considerable margin. At both these rifles' inherently limited range, weight trumps the pointy bullet as a hunter. (Hornady's Leverlution bullet/cartridge makes any theoretical x39 range superiority moot anyway if you go that route). The "point" here being, I'd choose the .30-30 over the x39 as a dedicated hunting rifle. Neither as a precision target rifle.
Best of both (.308 for "moose" (deer, elk) + lever for handiness) worlds to me would be a Savage 99 or Winchester 88--however, both out of production and out of your price range. Back to the .308 bolt idea, lots of 'em out there. Look for a used Savage, already a great value new, even more so used. Gret hunting and target rig in one gun.
THEN, if self/home defense becomes a priority, I'd look more to. pistol-caliber carbine to match a handgun in the same caliber....anything from the aforementioned Hi Point 9mm, .40 or .45 to a .38/.357 lever.