Yes, using the win98 approach, you can do with the IAone, just about anything you could with a regular desktop computer. However, it will be slower. If you were going to use it for yourself, and you were used to an Athlon 1.4GHz, you would probably be frustrated. But since it is for your mom, she might not care as much.
As for the screen, it does look very nice at 800x600. I have been running win98 on a 340meg microdrive and did not have any problems with the unit except that one day when the screen burned out - but compaq sent me a refurb and I sent that one back in. No problems at all with running the microdrive, and the usb ports seem to provide enough power to run just about anything (I have tested keyboards, mice, hard drive, web cam among other stuff).
Again, it runs it very well but just slow. Win98 won't fit on the internal sandisk, but jailbait will and of course, just plain DOS. You could get by with a 256meg CF or even a 128meg, but might as well just pay the $100 or so they are now and get the 340meg microdrive. That way you can have windows 98 (regular version and NOT just "lite") installed, with ms office (just powerpoint, excel, word - and no extra crap) and a 50 meg swap file, with lots of space left.
Now, since you have DSL, browsing will appear MUCH faster than over my stinky 56k modem. That will probably make a big difference on how fast it seems.