It's definitely possible to apply for all three at once, but I wouldn't tell them that in the interview............
If you want to go AAC remember that, unlike Dartmouth or Cranwell, you don't enter Sandhurst as a 'Pilot' - you have to graduate near the top of your intake for the AAC to consider you.
Other than that, think about what aircraft you want to fly and what branch you might consider if you get chopped before deciding on what service to join.
Oh, and most importantly, whether you want to wear a blue-grey, green, or black suit!
Good luck with the applications!