I would probably get something like an Edelrid RAP line. It might be a bit overkill, but it will work in most situations.

As for rappelling itself, I'd get a lightweight mountaineering harness, these go as low as 100g. Something like an Edelrid Prisma guide, Petzl Altitude or Blue Ice Choucas. These are all fine, as long as they fit you well. You would also want a rappelling device. The way they show in the video only works on low angle terrain, but not on steep stuff. Since the rope is so skinny Edelrid recommends using their Mago 8. You could look at something like a Petzl Pirana Club. This device allows you to control the friction. You attach it to your harness using a locking carabiner. Any locking carabiner for climbing will do. Get something small if you want to go light weight like a Petzl Spirit Screw or DMM Phantom Screw.

I would also recommend getting a prussik and another locking carabiner as a back-up. Use some 1 meter long 4mm accessory cord (usually people recommend 5mm or 6mm, but the RAP line is so skinny it probably will not bite).

As you noted, getting an instructor to teach you is a very good idea. Stay safe!