There's really not a lot in the realm of "specs", all Macintosh SE machines are the same, bar the RAM and storage options. They can come with 1, 2.5 or 4 MB of RAM and either one 800k floppy drive and a 20 MB hard drive, or two 800k floppy drives. The later Macintosh SE FDHD has one 1.44MB floppy and one 20 MB hard drive. This is the preferable machine to have because 800k floppies can only be read and written on other 68k Macs.
The more important thing to look out for is internally damaged/destroyed machines. Any compact mac is going to have a high chance of the clock battery exploding and leaking all over the logic board and the frame. Problems with the analog board and power supply are also common due to failed/leaking capacitors. Bad solder joints on the analog board and neck board are also very common due to the heat. The CRT having bad burn-in is yet another issue if the machine has high hours since people tended to not use screen savers on their machine.
In the worst case, you can end up spending several hundred dollars in parts for an old Mac SE to get it working.