I don't want to dissapoint you, but it would basically be pointless to upgrade this machine. You'll need more hard drive and memory, but that CPU is so old, and with the proprietaryness of the old HP machine, I would doubt it's ability to support it. I don't know what your gift budget is, but I'd say scratch the upgrading of this old one and look at a new budget PC. there are lots of decent ones out now for arount $500. Especially if you've already got a newish monitor. Then if you want to add on later, it'll be easy to put in an extra hard drive, another stick of memory, etc.
You can get a good value. I'd recomend looking for something with an AMD 64,or for even cheaper some of the new Semprons are coming out in 64 bit, and at least 512mb RAM. A good example is the eMachines T6412
at $499. If your dad will be shopping at Best Buy or Circuit City, Some other ideas are Compaq Presario (SR1630NX)
at $529.99 or the HP Pavilion (A1210N)
at $549. I say, have your dad get a budget machine and pull out the hard drive from the old machine and set it up as a slave on the new one so she can still access her files.