Thumb drive should work fine... however if the 98 machine doesn't have a CD burner... I'm sure it only has USB1.. which is really slow... IF it even has USB ports (if it doesn't.. then that thing is REALLLY old)...
XP can use damn near any file format. Fat32 (wind98) and NTFS... few other odd formats as well...
HOWEVER, i'd suggest NOT opening up an HP.. or any pre-built mail order computer almost ever.. unless you know what you are doing... First off.. they can tell you've opened it... in case you want to request warranty of some sorts... Second... pre-built systems are "cheap" because they use the cheapest stuff they can find... I.E. IDE cables with only 1 connection...
Jump drive should work fine.. however USB1 is slow... which is whats on the 98 machine most likely... and if its a LOT of files... could take some time... but thats the safest.. easiest way to do it probably....
One thing i'd consider if I were you guys as well... What files does she really need? Text / documents and such are usually small and should fit on 1 jump drive and be done... As for programs... you are better off downloading new versions.. or installing them fresh.. rather than just copying them over and trying to have them work...
Best to have her only copy what she really needs and wants... The more junk you pile up on the new machine.. the slower it will run... I expect my computers to have 0 wait time when loading files.. folders.. and programs... when i'm forced to use public machines where I click on start menu.. or explorer.. and i have to sit for 10-15 seconds while it loads up.. I want to break something...