You don't mention which particular games you want to play so it's hard to make advice.
There's no guarantee that any particular one upgrade will help.
Adding more main System memory can help (DDR2?) but only if you don't have enough obviously. A better graphics card can help, but if you're bottlenecked at the CPU it won't matter. And vice versa.
*The best test of CPU bottlenecking is to open the Task Manager (Ctrl-Alt-Del...), start the game then either close it or alt-tab and look at the CPU usage under "performance".
If your CPU is hitting 100% then you are CPU bottlenecked at that point and a better graphics card would not help. Any time you are NOT at that point it does help.
This method is problematic with more than one CPU core however, but with one core it's accurate.
Other: It's very difficult to recommend spending much on this system. It might be better to simply search for games that do run well and are fun. Maybe try some DEMOS on Steam of older games to gauge your computer's performance.
With that speed of P4, I'm guessing DDR (hopefully not RAMBUS, in which case he's screwed). But he just wants to play older games on it, and the upgrade from 1 gig to 2 gigs of RAM would be the way to go.