Bought a HP a6200n. Now I want to add a nicer video card which requires higher power supply. Does it matter?

HP a6200n's power supply is only rated at 250W. All the video cards I look at require 300W or 350W.|||It makes a big difference. You will need to replace the power supply, hopefully it is a standard one. Many "retail" boxes have smaller proprietary power supplies that can't be upraded without replacing the case also. That might well be your most economical solution anyway. A case with a good power supply is probably cheaper than a larger power supply that might fit into your case.