Allyson, I had a reduction a couple of years ago now. A friend from work had it done and she looked great so that's how I picked my surgeon.
I went to the surgeon first for a consult and his office filled out and sent all the paperwork to the insurance company for coverage. I was denied the first time but then my massage therapist wrote a lengthy letter for me describing the pain and therapy I'd been through and next thing I knew, I was approved for surgery.
Insurance paid for all but approx 10% of the procedure, if I'm remembering correctly. I think my out of pocket was around $1,000.
Rather than losing sensitivity, I actually gained quite a bit of feeling in my breasts, which surprised me. They were heavy enough prior to the reduction that many of the nerves had just given up. Once they were perkier and lighter, the nerves came back to life, I guess. Anyway, sensitivity. Lots of it. The scarring hasn't really bothered me at all and I never had to drain the tubes myself. The doctor (or his assistant) did all of that stuff in the office during my follow-up appts.
Only real advice I have is to try to find a surgeon close to where you'll be recovering since you might not feel like a shit ton of car travel for your follow-up appts. I learned that one the hard way. And I think having someone helpful around for a couple of days to make sure you keep up on your pain meds is good practice. Staying ahead of the pain is easier than catching up to it.
If I can help at all with questions or concerns or what not, just let me know. Best thing I ever did and I wish I hadn't waited so long to do it.