Upgrading the PSU to 350W would only be necessary if you planned on going up to a lower mid-range video card (7600 GT comes to mind) That would definitely have an impact on gaming... and you should really consider some more memory... 1 GB is the absolute minimum for gaming with 2 GB being ideal. It sounds like you've got around a $200 project on yours hands if you upgrade all 3.
Your computer takes DDR so make sure you don't end up getting DDR-2 (the most common type of memory presently) and be sure to verify what type of slots (PCI, AGP, PCI-E) you have for the video card. Based on the age of your computer, it can't have a PCI-E slot... that's ok... AGP should work just fine for you. PCI? Well, that's a pretty wretched slot to be installing a video card... with PCI your options are limited and your performance will be as well.
Sounds like it'll be a good project.