Since I have a pretty small (40GB) hard drive on my PS3 I was planning on buying an external hard drive for some extra storage. I'm looking at a 2.5", 1TB, 5400 rpm Seagate Expansion with a USB 3.0 interface. Is this a hard drive that would work on a fairly old PS3 Fat with a CECHGxx serial number or do I need to look for a smaller capacity, USB 2.0 drive?
Capacity should be fine and I don't see a reason that you'd run into any issues.
Although from personal experience I would still recommend just (gently) ripping the external hard drive out of the case and putting it in your PS3. It's just cleaner and less clutter around your PS3 (plus you could put the 40GB PS3 drive in the external's case and have a small external drive if you wanted).
With that aside, I can see why you'd want to avoid that. So to answer your question directly:
As long as you have those, you should not run into any issues. You can go 7200 RPM, but many people don't want to add the small increase in speed for extra heat, especially on an older fat PS3. Capacity shouldn't really be an issue with current drives. I've found some sites stating that up to 2TB will work, I will try to find a definitive answer, but your 1TB will definitely be fine (I have that in mine). IF I remember correctly, it's mostly a limit on the Fat32 file system the PS3 uses, but I'm no file systems expert.