mostly newegg stuff...
could get a a7n8 delux for 125, mushkin 3200 512mb ram for 75, 2000+ for 59, some case with 300w psu for 40, hs/f for under 15 shipped (see the GC69 at SVC.com) radeon 9100 128mb for 72, dvd drive for 32, 80gb 7200rpm drive for 75
just under 500, should do it. later on more ram(another 512), a cpu (barton something) and video to upgrade (some radeon 9x00). save 150 or 200 bucks with the a7n266, 256mb ram, no extra video and a 40gb drive. you didnt mention a monitor, kb, mouse, speakers though...figure another ~250 for all that, a floppy and a cdrw instead of a dvd rom.
mechbgon has good suggestions in his link, others can be found.
Grisoft AVG has great free antivirus software. and
OpenOffice has a fantastic (for a free product) office suite for use.
edit: dont forget an os, xp home (pro is not necessary for a basic home user) is about 100 bucks or so.
linux is free, mandrake is very very functional with good hardware support, has plenty of apps (mail, browsing, word processing etc) and is super easy to install and get running with. may want to burn and let them try out Knoppix to see what they think. some people, even if theyll just do the same basic things, wont be willing to try a different operating system. and, some will to save some cash. i havent had any problems or issues with mandrake myself (though, id use an nvidia card, like the 4200, over an ati card due to better linux driver support)
as mentioned though, with a dell you dont have to be tech support, they get a nice pc, and its cheap, but not terribly upgradeable.