On Edit: Note - perhaps because of the embedded link, DU displays this post in a much wider screen than the current browser window so it requires scrolling to read it. Go figure.
The other thing to consider is that support is waning for XP, both the OS and products that run on it - including browsers. M$ doesn't even have an easy way to get SP1 for Vista now. I found it, but it wasn't easy. The frustration level may push her past any interest. My mom took years to recover from being stuck with a PS-1 (which sucked moose cock). Her husband was certain it was the only machine to buy because it was an IBM. Bad move.
If you really want to introduce her to web surfing, just get one of the low-end machines from OfficeMax or something. Sure, a little more expensive (but not much), but with support, warranty, current drivers, and hardware that isn't going to crap out anytime soon. Or you can order online - most have free shipping for laptops now. How about this one, HP Win 7 3GB machine for $399?:
http://www.officemax.com/technology/computers/laptop-computers-and-tablet-pcs/product-prod3210152?history=adfb8egb|categoryId~10004^categoryName~technology^parentCategoryID~category_root^prodPage~25^region~1@14o2hwr6|categoryId~283^categoryName~computers^parentCategoryID~cat_10004^prodPage~25^region~1^refine~1@qs8f4p3k|prodPage~15^refine~1^region~1^categoryName~laptop-computers-and-tablet-pcs^categoryId~325^parentCategoryID~cat_283@79g6by4t|refineName~Price^prodPage~15^refine~1^sub_attr_name~2^region~1^refineValue~399+%3C%3D++%3C%3D+578.99
There are a lot of options out there and the extra cost easily justifies the reduction in hassle and frustration you're likely to encounter with an XP laptop. For an experienced user, that's not such a big deal - I still run Win 95/98 machines. For someone who needs to be introduced to web surfing, go with a new machine. And immediately install Firefox - much easier for new users than IE (and much safer).