Okay, my new laptop has been ordered as well! I chose a mid-range Dell with a 17" screen, which should serve as a desktop replacement but be portable enough for the occasional business trip or other out-of-home work session (the reason I went with a laptop rather than a desktop - I don't think I would have wanted aything smaller, though). I'm not sure about battery life - given that it's on the larger side I suspect battery life won't be more than a couple hours, but I don't think I'll be working too often in places where I wouldn't be able to plug it in, so that wasn't really a top concern for me.
I've decided the old laptop won't be "uncluttered," but will be given to my children (ages 7 and 3) to use on the days they are with me instead of their father. They are both very interested in computers and can have fun banging around on it as long as it's still basically functional, and I can store it out of sight in an empty drawer (something I have plenty of after uncluttering my whole apartment!) when it's not in use so it doesn't take up surface space. And if they spill something on it or pop off the keys - not a huge deal. (The new laptop will be off-limits, though!)
All in all, a good solution, I think. Thanks again for everyone's support in allowing myself to enjoy my new life!