The first laptop based frame I put together (I'm working on my third right now) was an IBM Thinkpad 560E. There were several reasons that made this my first choice:
1) It can be gotten pretty cheaply online (got mine for ~$50).
2) I found a site here that basically told me got me on the right track and has some good pictures of disassembly of the 560E. It had a link to another site called www.misterart.com where you can get a plastic shadowbox (~$8) in which a stripped down Thinkpad 560E fits perfectly. I also got my libvga.config from this site, but there's more about that in the software section.
3) It looked like it had everything I needed to make a quality frame (close but not quite). The minimum requirements I was originally looking for were:
a) Hard drive big enough to put a lot of pictures on and load linux (minimum ~2GB)
b) PCMCIA port so I could use an old linksys ethernet card I had lying around. (If you want to buy one, here is a link to the one that worked for me: Linksys PCMPC200) You need an ethernet port for 2 reasons. First, the best way I found to load the OS was the netinstall version - you basically load a very limited version of the operating system on the machine then connect it to the internet and it guides you through the rest of the installation. It also lets you easily get the software you need onto the computer through the apt-get install command in debian. Second, if you want to reconfigure your frame once you've got it all done, its a huge pain to disassemble your entire frame just to use the keyboard and screen. If you have an ethernet connection, debian lets you easily install an SSH server on the machine (takes minimal resources) so that you can SSH remotely into it to reconfigure as necessary. Additionally, I used the ethernet card (by way of SSH) to get my pictures onto the frame - much easier than floppy or CD transfer.
c) Floppy drive or CD drive - CD drive is easier if you have a slow internet connection because it lets you load a lot more of the necessary netinstall files from the CD. If you have a broadband internet connection, a floppy drive works fine - it just takes a while to get the install files (I think it took me around 10-15 minutes to do it from floppy).
d) A good screen is key. This is the part of the computer that everyone is looking at. Make sure when you buy your computer that the screen is not too dim and that it doesn't have any dead pixels.
In hindsight this is a decent laptop for a basic DPF. The screen is good and once I got the software right it has run pretty well. The main reason I didn't try for another one for my second DPF was that it doesn't have a USB port - a handy feature for getting new pictures onto your frame rather than using SSH.