<B>As far as your current specs go</B>, Truthfully, you can get away with what you have.
I also upgraded fom win98 (this was SE) to winXP Pro and had:
-128MB SD RAM PC133 upped to 640 MB of RAM
-new 80GB hardrive
-13.6GB hardrive became my 2ndary
speed was fine. I had to disable the translucent selection rectangle effect back to the classic dotted line square found in win2000 and before since it would bring my system to a crawl when it got bigger than 320x320 pixels. Everything else ran OK. Not as smooth as win98 SE mind you, but it was still acceptable.
RAM was fine too. IIRC, i had 128MB at first, but I upped it to 640MB. There was a slight performance boost, but it could've all been in my head.
I tend to store lots of music, PC game files, PC games themselves, media, and other stuff on my PC, so I needed more than the 8GB available after winXP installation. It'll greatly vary by what you do with your PC. For some, 5GB free will be more than anyone will ever need. For the digital or industry person, they can really use 500GB+. Get familiar with your mother's PC usage habits to determine if another/bigger hardrive is in order.
Just keep in mind, after install, winXP eats up about 2GB of space, but there's more to that. Using System Restore eats up space depending on how far back of a system state you want it to store. Virtual memory, and temporary internet files all use the same space. I'd say give assume 5GB of all uses for winXP, required as well as some optional ones that are good to have just to be on the near safest side.
If you want more optimum performance, say...
-somewhat faster but definately more noticeable speed
-better multitasking (5 browser windows, 3 Office documents, some more complex apps like video player, and better performance due to less virtual memory use)
-more headroom in terms of freespace.
I'd say get at least a P4 2GHz and 512MB of RAM. The processor is likely a stretch, but RAM can be easily updated. Even a 512MB stick of RAM, giving 768MB total is a cost effective, and easy Do It Yourself upgrade.
<B>Alternatives to upgrades</B>
Many home users like winXP for sure, but for the sake of performance, consider getting win2K. win2k is considered the best Windows OS from an IT standpoint. It's got the best features for such low requirements. WinXP is superior, but only if you have the hardware to run it. Coporate environments prefer win2k since they won't need as high of hardware to get it to run as smoothly, but also mentioned by the other poster, winXP does have some issues that can still be problematic. These are moreso for IT admins.
If you really must stick with winXP, then consider turning down all the special effects, the winXP interface (will be replaced with the classic win98/win2k interface), and other visual effects. If you will have issues with your posted setup, doing all that will reduce the load on your system resources enough to make things smoother for sure. Without all that "bling", winXP is just win2k with better networking built in.
win98 ain't bad, but i had several lousy moments with it during my 4 year with it. Granted, i could've taken better care of my PC on the inside of the hardrive, but I do feel winXP is better in that regard.
Some of your apps may not work. I tried changing the .exe properties of certain apps to win98 compatibility, but that didn't work. Was able to find either winXP compatible versions or winXP equivalents of the apps I used to use on win98. My flight stick only works on win98 tho, and I may replace that one day when I get back into flight games. So yeah, keep in mind, some of your hardware and software may not make the leap across. Most likelythe former.