1. Athlon II X3 ($70-80) or X4 ($90-100)
You don't have many choices in this price range, but these Athlon processors are affordable and quite capable.
2. Any AM3 Motherboard ($35-90)
AM3 motherboards are the best value, starting at just over half the price of the cheapest Intel motherboards ($35-50). You may want to look for one with USB 3.0 ports if that feature interests you, but it will cost more ($70-$90).
3. 2GB (2 x 1GB) DDR3 1333/1600 ($40-50)
A new motherboard will require new memory. DDR3 has come down in price but is still not cheap. If two sets of memory are the same price, choose the one with the lower CAS latency (this is as important for performance as the frequency/speed of the ram). Unless you overclock the CPU, the memory will only run at up to 1333 MHz so DDR3 1600 isn't necessarily more valuable to you (you may be able to lower its CAS latency by one or two points at DDR 1333, however).
4. Nvidia GeForce GT 240 ($50-70) or ATI Radeon HD 5670 ($70-90)
Highest performance graphics cards that don't require a PCI-E power connector from the power supply. If the power supply has not been upgraded, these are the best graphics cards you can get.
5. Samsung Spinpoint F3 or other 7200RPM 500GB ($40-50)
The Samsung Spinpoint F3 and Western Digital Caviar Black hard drives are among the fastest. The capacity can make more difference than the brand, though. Hard disks with higher density platters are faster because the data is stored closer together, is easier to access. Don't try to save money by buying a hard drive with a capacity smaller than 500GB.