512MB should be fine. 350MHz is slow relative to current processors, but the processor speed is not the overwhelming importance it once had. the important factors are:
processor speed - but the gain diminishes as the speed rises. going from 1GHz to 2GHz will not double the overall performance.
memory - same story. if you go from 510Mb to 1024Mb, for example, you won't gain if what you do doesn't touch the extra memory. on the other hand, too few memory is crippling. and the applications become more memory consuming each year.
disk speed - this is one thing in a computer that tends to wear out faster than the other components. you can regain a bit with regular maintenance (defrag, remove unneeded stuff), but not much.
a graphics board will go a long way to reduce load from the processor and memory.
"Does that mean that its memory is full quickly?"
exactly. set up an xp computer with a minimum necessary for autodefense (a firewall and a resident antivirus). boot and have a look at the task manager - 130megs of memory already taken.
when you play games here, you use a browser; how much memory that takes depends on what browser you use, and how many sites you visit. if you go and visit sites that use java, or flash, or pdf pages or... your browser will load each one in turn. and even if you unload the pages, some of the allocated memory remains resident. xp is better in this respect than some of the older microsoft marvels - once you unload the browser, you recover most of the memory that has been allocated.
still, don't bother with xp unless you have 256 megs. and even so you'd wish for more.
don't even think of it. XP is very memory hungry. with no application running I have close to 128M occupied after boot. anything less than 256M, you'll find yourself swapping all the time as soon as you try to execute anything.
the only "remedy" is to pass your time with a regcleaner or some such, hunting for those dll's and other junk cluttering your system at startup.
YES!! hidden keys, like the clicking on the opponents left cube while simultaneously clicking control, "a" and the F12 key with your left toe, which turns your throw into a double-6!
<there are also some hiden MS files and folders, which are used at ths system's discretion. one is the recycler, the other is "System Volume Information". you can see them by unchecking tools->folder options->view->mask exploitation system files (this is not recommended)