First, you're talking about an HD 7750 GPU, no need to specify "Powercolor." It's not really relevant but the way you're talking about it makes me feel like you think you need to get a Powercolor HD 7750. There would be no difference if you bought a Asus HD7750 or Powercolor HD7750, aside from size, color, and fan.
Second, for ~$99, you'd be getting a better bang for your buck with a GTX 550ti, however if I were upgrading my GPU, I'd be dropping a little more money on a GPU. Nvidia is also generally better for GPUs, although AMD/ATI isn't bad. AMD/ATI just hasn't caught up yet with Nvidia (however, AMD/ATI is close, especially with its HD7970) and Nvidia PhysX is supported by more games.
Third, you need to post your computer specs. If your PSU can't output enough power to power for GPU, your GPU won't be running at it's full power, but it shouldn't damage your GPU. Your processor should also be powerful enough to support your GPU so you don't have any bottlenecking. Your motherboard should also have the correct slots for the GPU (which it should).
