It really depends on if you're just going to play games and Blu-Rays or if you want to do 'extra' things like play PS2 games or install Linux.
I have a 20GB "fat" PS3 (now 160GB) that I bought on November 18, 2006, the day after launch day. To date, I've had zero problems with it. No overheating, no problems reading games, nothing. I credit that to good Sony engineering and actually putting out a product ready to be marketed (cough Xbox 360 cough). The "fat" PS3 does use more power, but I'm not sure it how much of a difference it really makes in the grand scheme of things.
I've only played PS2 games a couple times, never with any problems, but it's not something I care that much about so it's not something I'd really miss. I've also never installed Linux on my PS3 but I kinda like the idea that I could if I wanted to.
The only thing I dislike about my PS3 if the lack of Wi-Fi. Mine is the only model to ever be released with that capability, and it's annoyed me a few times, but overall it hasn't been a huge problem. But even if you do buy a "fat" PS3 you'll likely get one with Wi-Fi since the 20GBs weren't that popular and were discontinued fairly quickly.
Also, I'm not sure if this is true or not, since I've read opposing opinions, but it may not be possible to upgrade the HDD in the slim PS3 (if I'm wrong someone please correct me). This is a very valuable feature and one of the great things the PS3 has going for it. It was SO easy to upgrade the HD, like, easier than to do so in a MacBook, and also very inexpensive, since they use the same 2.5" SATA HDDs that Macs do.
So, in conclusion, it probably doesn't matter which you choose, especially if you're only going to use the basic functions.