From what I know (which isn't much, so take it for what it's worth).... if you are married or living common-law, your stuff stays put until you're through basic and trades training, and then they move your home and family to wherever you are posted.
If you are single, and have a house/apartment/things that need packing and storing, then they come before you're in basic training. The reason being is you are likely going to SAVE money by not paying rent and instead, you pay rations/quarters at basic and your trades and other qualifications. Your stuff stays in storage until you are given your posting. Depending on the length of training, time inbetween courses, you could theoretically be "away" for a year or more. From there, you get to decide (generally, from what I've heard) if you want to stay on base or if you choose to rent/buy a house/accommodation elsewhere.
The "shacks" vary from base to base as does the price, from what I've understood. I have heard people paying less than $100 a month but they share a room with someone else. If you want your own room, it's a bit more. Then there's a difference between officer and NCM accommodations at some places. If you are living out of a suitcase, this could be an excellent way to save up some cash, especially if you think you are going to be on training a lot of the time. Why pay $1000 a month on an apartment if you're going to be gone significantly for extra training or time in the field?
For myself, I have enough furniture for a house and as well, have a cat and dog -- not really acceptable in the 'shacks'! But I likely will try to get a regular apartment on base where you pay more and have less restrictions. Prices for this are roughly the equivalent price of housing/market price in the area. However, I will also look off-base for housing. My ex (who was army) did not want to live on base because he liked being able to 'get away from work'. We lived off-base for the six years we were together and it was our preferred way at the time. Where you choose is up to you I suppose. All I know is, I've been in a "transient" state since February 2009 and the thing I most look forward to is having my own place again! So yes, definitely am taking the packing/storage route and definitely am looking for my own place.