Hmm. apparently some of the Sapphire cards also support legacy BIOS and might work with this system. What Radeon chipset would give decent performance without breaking the bank? With an emphasis on not breaking the bank.
I'm using $130-$150 nVidia cards (GTX 750 Ti and a GTX 950) on approx. $500 Dell machines and getting 55-60 fps in AH3 beta. To me, that is acceptable performance for a low-budget choice.
Comparable Radeons are likely also in the $130-$150 range on Newegg, maybe these (according to Tom's hierarchy chart):
HD 7870, R9 270, R9 270X, R7 370
HD 4870 X2, 6970, 7850, R7 265
HD 4850 X2, 5870, 6950, R7 260X