Upgrade pc hardware? a few question?

For strictly an increase in speed that would be the processor and the RAM. If your are looking for better FPS on games than I would say Processor, RAM, and Graphics Card. Your 600W power supply would also benefit from being replaced if you upgrade to many things you may not have enough power. The ATI 5770 is a great GPU so I would keep that unless you are a hard core gamer. I would get rid of the Core 2 processor and look at either the Intel i5 or i7 processors. Your ram is 800mhz which is fairly slow in todays standards so I would consider replacing it with ram that will run at the around 1200mhz. The processor cooler you list is the one that came with the processor I take it? If it is get rid of that pile of crap and get a better one for around $50.00, any brand it doesn't matter.