Add me to your growing list of people who DMed their first D&D experience. I got the 3.5 starter box when I was in my early teens ('04?), ran it for three of my siblings. I ended up just running that for sometime, shoehorning in extra levels from the PHB (the box only supported levels 1-2!) so we could have characters for longer but without added complexity.
Personally, I'm pretty happy with the Starter Set taking place in an established setting, period. When I get my copy of the Starter Set, I'll be running it for people who've never played D&D before, and being able to take their characters from the Set, and continue play in the world without my needing to homebrew a setting takes a lot of work of my shoulders. Unlike with experienced players, I won't be worried too much about screwing something up about the Realms' history, either. This seems pretty ideal for me.