In ANH, Luke wants to apply to the academy. For a long time, I assumed this was some sort of secret Rebel Alliance academy. However, recently I have heard people say Luke was referring to an Imperial academy. This does not make much sense to me. First, Luke tells Obi-Wan he hates the Empire. Second, Luke becomes excited when 3PO tells him he and R2 had been part of the Rebels. Most importantly, Luke tells Owen he said "next year" when Biggs left. This implies Biggs went to the same academy. We see Biggs at the Rebel Alliance base on Yavin IV. Thus, I assumed Luke was referring to some sort of secret Rebel academy. What do you guys think about this academy?
That said, the Academy has different levels - and joining the Academy for training doesn't necessarily commit you to joining the Imperial military - "Merchant Service" is an option: http://starwars.wikia.com/wiki/Imperial_Academy
I think Luke wanted to join the Imperial Academy to get the hell off Tatooine. As he said, he doesn't like the Empire, he hates it, but there is nothing he can do about it right now. As far as Biggs, he got trained, then defected and secretly joined the Alliance, pretty much what Thane did in Lost Stars.
It does raise the question of whether Owen's refusals are motivated by knowing that Luke going to the Academy will result in Big Trouble. In Rebels, we find out that the Inquisitor analyses Academy performances at the Lothal academy - and when there's hints that a candidate might be Force-sensitive - he finds out for sure - and delivers them into Project Harvester. We don't know how much Obi-Wan told him - but I could see him having been told that "The Empire's declared Jedi outlaw - don't let Luke son of Anakin come to their attention."
LUKE The Academy didn't change you much...but you're back so soon? Hey, what happened, didn't you get your commission? Biggs has an air of cool that seems slightly phony. BIGGS Of course I got it. Signed aboard The Rand Ecliptic last week. First mate Biggs Darklighter at your service... (he salutes) ...I just came to say good-bye to all you unfortunate landlocked simpletons. ... BIGGS I made some friends at the Academy. (he whispers) ...when our frigate goes to one of the central systems, we're going to jump ship and join the Alliance... BIGGS I know it's a long shot, but if I don't find them I'll do what I can on my own... It's what we always talked about. Luke, I'm not going to wait for the Empire to draft me into service. The Rebellion is spreading and I want to be on the right side -- the side I believe in. In Brian Daley's radio drama "exploration" is another job opportunity next to the "Merchant Service". The Anchorhead scene in ANH suggests that Biggs joined either "exploration" or the "Merchant Service" (according to the ANH novelization Rand Ecliptic is a freighter). I think it's obvious that the Academy is an Imperial facility which probably allows individuals to proceed with career opportunities but can also draft aforementioned individuals into military service.