If your mum Doesn't have a pc, this would be a great start.... Set up an email address, get her on the net.... But there arn't many apps for it... Unless you run windows or linux.
My mum uses the shared pc in the hall some times. I was planning to install xp on it but I'm afraid the wi-fi appear afterwards but usually my mum uses it to chat on msn and look at carzone.ie
I believe it is all Celerons, but I have a friend who just got one (4G), and installed Windows XP onto it, and is really pleased with it, he says its fast and is well worth it.
I've used an Eee PC and a Celeron is good enough, just because it's a Celeron does not automatically mean you can consign it to the 'rubbish' pile. It uses a very light Linux flavour so it doesn't need brute force. It probably boots faster than your laptop too.
When I saw the thread title, I immediately thought "eee PC"
Of course, when buying any gadget it's always best to think first of what it'll be used for. I'm sure you know about your mom's computer habits more than we do. Most older people (actually most people in general) are happy if they get to type documents, check their email, and visit their favorite sites. Which I think the eee PC is perfect for