So, thanks to Hajo, I've had the chance to try out a 2GB GTX750 Ti in AHIII, and though I've used it only a couple rounds today, it seems to be working quite well with my system. I'm routinely getting 59-60 fps in flight with default settings. In combat close to ground level this dropped to a low of 45 fps, but I brought that back up to 55-60 by setting the environment slider to zero (Could have left it, frankly... 45 was very temporary and still playable, but I want as many fps as possible rather than eye-candy).
Just like Skuzzy said, I can confirm that even with all the settings turned down, it still looks better than AHII, though even with this middle-of-the-road card you don't have to drop everything to zero to play.
Just for reference, I'm running a quad-core I7-4790 (3.6 Ghz), 24 gb ram, and Windows 10. Display is at 1920 x 1080 resolution.
So if anyone else is on a budget, the 750 might be worth looking at. Min recommended power supply is only 300W, which means you there's a good chance you just drop in the card & go. I have a 460W psu stock, and it works great.