Is it seen as an advantageous career move? Yes--mandatory.
Is their a wish list of sorts? It is really pretty much wrought--first staff tour is usually at a minor staff (Capt-Colonel Command) The others are usually flag staffs.
Is it your choice of when or does it follow a natural progression? You have some choice--but it is usually about trying to avoid the Pentagon or a FOUR star staff as long asd possible :)
How does it affect the Team when they get a new commander? Depends on the Commander(s). If the outgoing guy was well liked, then the new guy usually has a bit of a hard time living up--if it is the other way, the new guy usually has trouble getting people to trust him--all in all, unless things were estatically god or miserably bad, switching commanders has minimul effect.
Also just curious can you/have you done tandem parachute jumps? I have not--requires a lengthy special school that I was never that interested in.