I bought the GF's grandmother a laptop last year (with her money, of course) and she's very happy with it. Keep in mind, what we want in a computer isn't going to be what the family member needs in a laptop.
She goes online for email and web games and that's about it. Just about anything you get is going to fulfill this purpose.
I bought her new laptop online at walmart.com for $700 including shipping and tax.
The specs:
AMD Sempron 2600
256 MB DDR333
15" XGA SuperBright LCD
40 GB HD
DVD/CDRW
Build in Wireless/NIC/Modem
Just shy of 7 lbs
For her this was a perfect computer. Moderm and nice looking, she's not had any problems with it at all. She used to be on AOL but when installed had major crashes/problem. I removed AOL and set her up on PeoplePC and it's been running great since. (She needs the front-end portal these companies provide). The only technical support I've had to do is operator error stuff (She's 92, so that's to be expected). She did complain about bumping the DVD button and it opening too much.. a piece of scotch tape solved that problem.
Yes, it's a wierd off brand, but as you may be aware, most companies actually rebrand laptops from other companies. This is just another example. It's the hardware that matters at the end of the day.
http://icpowerhouse.com
I have several other laptops as well and they are all decent except for one (more on that below)
I have an old Dell PII/366MHz/192 MB RAM that is used as an internet computer. Been going strong for several years. Even runs XP Pro just fine.
I have a HP PIII/850MHz/256MB RAM that I take whenever I go somewhere. The hinges stiffened up to the point where I shorted something out inside the laptop when I open/closed the lid, but it still works decent if for an occational freeze. This has been a workhorse for several years as well.
I also have a Sager PIII/1GHz/256MB RAM that works fine, except the battery died on it within the first year of ownership. replacing it would not be worth it so it sits plugged in all the time as test computer for messing around. It's a bit slow for what it is.. the HP out perfroms it, but could be due to shared video memory.
All 3 of these latops I've had (or belonged to family and have supported) for several years. I've been happy with them all for the most part, at least from a "user" point of view.
-Ryandor