If your iBook was still behaving properly, I'd say go for some desktop version with a big drive on it ... you can have it doing misc. whilst traipsing about. (Mine has played dead a handful of times too, but rarely. I had assumed it was due to the extreme cold ... I've had to haul it around even in this weather.)

I mean, I've still got a Pismo that's hanging on there by a thread (erm, if you're new to Mac at the iBook stage then, lemme see ... that's about an 8 or 9-year old Mac PowerBook) and it definitely has power management problems that basically make it impossible to use as a true laptop, but with a replacement power cord and a USB drive, it does okay ... and the kids make great use of it.

For lower-end Mac desktops, I've used and quite like both the current iMac and macMini ... solid OS and cheap. I've got one mini doing work 24/7 and doing so brilliantly without fail. I bought the iMac recently as a recycled demo model, so got a few hundred knocked off the retail. It was still new enough to qualify for AppleCare, so as far as I'm concerned, it was a great 'risk'.