Hey, congrats on your new purchase!

My first convertible was a 90 LeBaron and I loved that car! I had problems with mold growing on my top since it was parked outside 24/7. At the time I used Dawn and a soft brush to clean it off... Looked good as new too. That was in pre-Autopian days, so I'm not sure I'd suggest Dawn. You might try Raggtop brand cleaner and a soft brush, that's what I use now on my convertible Vette. You'll find everything you need here:
Convertible Top Care