In real world terms, the US Space Force will without question be an evolution of the Air Force: it is already happening. Space Command is one of the USAF top-level commands and already has a substantial mission and budget. As time goes on they should have no problem in maintaining control as technology and the mission changes.
On the other hand, if we ever run into an alien FTL drive that we can adapt to build starships, the Navy will jump to the front of the line. In that case, the first Starship Captain would likely be an ex-pilot Carrier Captain. Probably one with an odd fondness for 80's rock like FINAL COUNTDOWN.