Thats good advice from cranberry ,…. you could keep your case, HDD, DVD drives, Power supply etc just ensure your existing power supply will power you new components. You'll require Motherboard, memory and graphics only …. In this case.
If you want bang for buck you can also get very good results from overclocking lowend hardware. Cooling could be an issue here make sure you do a bit a research before attempting anything that you are not in the know about. There is lots of info online (Google)
For components or prebuilt systems (gaming) i would recommend the following …. I have been using them for years
Link
Hope this helps