A word of warning:
eVGA recommends at least a 400W power supply for the 550ti, with at least 24A at +12V: EVGA | Products | EVGA GeForce GTX 550 Ti FPB | 01G-P3-1556-KR
It appears to need a 6 pin PCI-E auxiliary power connector as well.
The XFX 7750 wants at least a 450W PSU.
These are both good cards for their prices, I guess, but I'm not sure how well they'd work with the 300W power supply of the HP. I expect that the PSU could be upgraded, but that will raise your budget, plus the amount of effort required. (Are there any warranty issues?)
I don't own the games that you mention. For the Batman
title, these are the hardware requirements: http://www.geforce.com/whats-new/art...ents-revealed/
The minimums are an nVidia GT 8800 or Radeon HD 3800. These are old; I don't know what current cards are comparable.