Will this be fast enough with the specs of this desktop?

It's fast, but far from fast fast. I'd up the RAM to at least 3GB...4 would be better. And the graphics card could use an upgrade; for "fast fast" anyway. I translate that into meaning gaming computer fast. For what you listed in your needs/uses, I think this computer will suit you very well. I'd also agree to go with Windows XP if you can.