Horses have a 60' move speed and come with Disengage for free (or Dash for 120 but then you provoke AoO).On your turn you can disengage with your horse and then fire away.
Beastmaster Ranger looks good (with DM permission to select a Horse). Order your companion to let you command it instead of using its own Initiative. You can always get it to act independent as well.
This way your steed gains HP and HD and its stats increase as you do.
Take archery style as your F/S. Hunters mark naturally. Mounted Combatant is still pretty decent to take (for the survivability of the mount)
For tricks, consider 3 levels of Battlemaster Fighter after hitting 5th.
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