I agree with both Rincoadeje and Asolfr, particularly with Asolfr's comments on compulsory military service.
I have 2 main points to add:
1: An argument could be made for compulsory service in a "civil defence" unit- such units on earth do not fight but handle fire-fighting, floods and other natural disasters.  In space they could be trained to handle decompression caused by structural damage, accidents or attack, as well as chemical spills and fires that pose a bigger threat on a space station than they do on land.  The argument for compulsory service in this unit (at least initially) is that in the early days of Asgardia, everyone will need to know how to respond to such events.  A decompression may need to be dealt with by whoever is physically closest to the breach when it occurs, rather than being able to "call a fire-fighter" the way one would on Earth.  Whether this "civil defence force" is connected to the military at all or whether it runs under a separate emergency services ministry is an entirely separate debate.

2: In response to Asolfr's comments about maintaining an army that is not compulsory without paying a lot, perhaps a good initial payment structure for the majority of the army would be the model used by "reserve" military forces in Australia and many other countries.  These services are can be volunteer or compulsory (I would lean towards volunteer unless absolutely necessary) and staff are payed for the time they spend training, and any time they spend on operations.  However, they do not work for the army full-time, but after an initial period of training they return to their day jobs.  These staff are not payed by the army again until they return for further training (which is frequently 1 night a week of minor duties/training and 2-4 weeks per year of more concentrated training) or are deployed on operations.  This would seem a sensible method to maintain a pool of skilled staff that could be called on as needed (whether this need arises because of military tensions or because of predicted solar flairs or meteor showers) without breaking the bank.

In response to Mech1031's comment on drones, image processing software to distinguish between armed and unarmed opponents will probably be available by the time we can build such drones.  The bigger problem from a military/security point of view is that they could be hacked or jammed.  However, for defence against non-military threats (meteors, space debris, solar flairs) drones in an anti-aircraft type configuration could be idealand such drones could protect against raiding parties or invasion as well.  Especially since such drones could be connected to their control centre by cable instead of by radio transmission, making jamming or hacking extremely difficult.

As a former soldier I have few ideas.

1) First of all I think that until we see what exact threat we're dealing with the army should be built from volunteers but be a paying job. No mandatory service as we will need human resources in a lot of other areas. Only in a case of emergency it should be mandatory to grab a weapon, at least for the beginning - you can't maintain a working army that is not mandatory unless you can pay a lot, or have a really big population. And sadly - we won't have such big population or so much money to give.
2) The structure of ADF. I agree with rincoadeje - there should be 2 Battalions: Asgardia Defence Forces and Space Defence Forces. One will protect the station and the people on it and the other one should be more of Outer Space army - like in the Navi there are troops that protect the territory from the sea sides on land and troops that protect the territory from sea side on sea and protect the water territory. I don't know if ADF should be at the same time the army and the police force. But it's an other question for later. Both DF should have 2 (I'm sorry if it's hard to understand because of my English) wings or branches - Space Force and Land Force, as they both will need to fight on land and in Space/Air or against a threat from Space/Air. Of course there should be small branches going from this two such as cyber-fighters, Search and Rescue, anti-space forces and etc.

This all I had to say for now. I will add more in the future.