I agree with just about all of the comments regarding starting on Baritone. Just remember that it's the 2nd heaviest front carried horn in the line.
I started on trumpet, then went to baritone after I got braces. Frankly, I missed playing the melody, and high notes, and went back to trumpet and mellophone a year later. Yeah, there were a few shows where I got some blood out of the spit valve, but oh well. The braces were the worst with cut wire pointing outward.
I started my drum corps career with SCV on 2nd Baritone. I eventually lead soprano with SCV in 1981 with my braces still on. After I got the braces off, I completely lost my lip. I joined The Blue Devils and played LFL-Soprano (4th) to get my lip back in 1983 - no more baritone for me. The following year I was joined the ranks of the famous UFLS.
As for the private lessons - I would say worry about that AFTER you've decided that brass is your instrument. I didn't take my first private lesson until I was a senior in high school.
You'd do well by contacting my friend Mike Quillian with the Oregon Crusaders (shameless plug). Mike, like me, is an alum of the 76th Cavalry Band - Indepedence HS, San Jose as well as an undefeated DCI champ with the Blue Devils (79, 80, 82).