Do NOT do an upgrade - you will be sorry. It may go OK, but chances are good it won't - or there will be all kinds of quirky things that come up in the future you won't be able to fix.
To run XP - now that they have SP2, you need a minimum of 256MB RAM. In the old days, 128 was enough to get by, but with the latest patches and security updates, the base OS is up to 142MB RAM now.
I would not run anything less then a Pentium III 600Mhz either. If you are not going to do any pictures and video, a 40GB hard drive is enough to get by with a fresh install.
If you do not meet any of these requirements, just replace the box. I don't prefer Dell, they upsell everything and before you are done, its $800 for a PC. Gotta pay for those million dollar commercial spots and bail for the "Dell dude".

I can get Compaq's from Microcenter for $279-$319 all day long. They run AMD 3100+ processors with 256Mb RAM and 80GB HDD. A perfect "parent's" machine IMHO. For the basic web browsing, wordpad typing, emailing older person, its more then enough horsepower and it comes with XP Home, which is fine as well.
Thats my real world experience rolling out machines to the "training wheels" crowd for years.