what should I know before buying a 355 spider?

You should probably start off by doing some searches as these topics have been covered many many times. Good luck and welcome.

 

I'll do my best and help with the searches:

1. Some do and some don't. It seems the seat potentiometers and old fluid in the system are the primary (but not only culprits). Occasionally, a ram will go bad but I would try replacing the fluid before replacing a ram. Lots of threads to read on these three topics.
2. Rarely. We get suspension warning lights every now and then but it's usually the shock actuator and not anything wrong. Easy fix but do a search on 355 shock actuator or 355 suspension warning light and you'll see lots of good info.
3. Very rare issues other than simple clutch replacements. Good news is that it's a DIY job. The manual gearbox guys can chime in here but the gearbox appears to be pretty bulletproof.
4. We're starting to see more and more evidence of the connecters in the engine bay causing CEL lights. The good news is that Dave Helms has developed a kit to remedy this problem. I'm getting ready to order one myself and just need to get off my duff. Do a search on 355 gold connector kit and lots of good threads there. The kit also seems to really help in the performance and drivability as well. Outside of that, nothing comes to mind but others may chime in as well.

I hope this helps.

 

I recently purchased a '97 F355 Spider 6spd. You are gonna LOVE it!! My car at least, shifts perfectly and is so satisfying. I didn't even consider flappy paddles. Its also the best convertible I've ever been in. No wind buffeting at any speed. Good Luck, and congratulations.

 

With a $32,000 service bill, I would think you are covered

 

I'd agree with that. Especially if the bill is from someone reputable.

 

I forgot one thing on the gearbox. The seals in the throw out (TO) bearing can be occasionally problematic on the factory unit. It doesn't happen often but every now and then you'll see a post from someone who's TO seals blew at an inopportune moment. Check to see if it was replaced with your service. Ideally it was replaced with a unit from Hill Engineering. I'm assuming you're already familiar with their products given your 360 but they make really good stuff. If they did replace it in your service it's usually a good idea to replace the triple seals at the same time.

 

that seems to be either a really bad car or a very inflated number.

IMO, you should find and buy the best documented and serviced car possible. (it's a lot harder than you think).

This is a good starting point:
http://www.the355.com/mambo/index.php

 

$32k service bill?

yikes. Makes me think twice about looking for a 355. Although I suppose those bills don't come around THAT often, but still....