Let me try to answer your questions.
1. What are the primary employment areas for junior officers?
The primary employment for junior Naval Logistics Officers is in support to naval operations, be it on a support base, in headquarters or in a ship. All of your initial training (after basic and second language training) is focused on the duties and responsibilities of a Ship's Logistics Officer (AKA Supply Officer or SYO although responsibilities are not limited to supply). In the ship, you are responsible for all logistics support, which includes supply, food services, finance (both public and non-public) and transport. You are also responsible for the RMS Clerks in the Ship's Office who are in your Department, but they largely work for the Executive Officer. Employment in HQ and on the support base is generally in the same areas except for transport and food services (unless you are also specifically qualified as food services officer).
2. How often am I away on training, at sea, just not able to come home at the end of the day?
It really depends on your circumstances. All the training that has to take place before you get to your first ship can take upwards of two years from the point where you're sworn in. After Basic and Second Language Training, you will have to do a common logistics course with your Army and Air Force brethren. Then you will have to do the actual Sea Log course. You will also have to do a sea environmental course (damage control, firefighting, difference between the sharp end and the blunt end, etc) and a naval operations course. After all the courses are done, you are finally ready to go to sea at which point you will be posted to either Halifax or Esquimalt, if you're not there already. You will then be employed somewhere until a training billet becomes available in a ship. Up to this point, after basic, you are essentially home every night. If your family is with you, life is good as long as they don't interfere with your studying. Often times however, your family will be on one of the coasts and you will be in Borden on course for several weeks at a time (last time I checked, the Sea Log course was either 10 or 16 weeks).
Once you get to the ship, you start an "apprenticeship" of approximately 10 months where you act as the "baby" to the SYO. You can expect a number of trips over this period, sometimes for a week or two, but you can usually count on at least two trips of up to two months. You can also end up in a ship that will do a six month deployment. The reality is that you want to sail as much as possible in order to get the experience. Over the course of the next ten months, you will work in all the different Divisions of the Department and you will have a list of requirements which you will have to complete. Finally, if the SYO and the Captain feel you're ready, you will sit a board where a bunch of senior Naval Logistics Officers will grill you for two to three hours on what you have learned. It's actually not as bad as it sounds - plenty of us have survived. Once you pass the Board, you are then considered fully qualified and employable. You have also joined a pretty exclusive club. Your next appointment will likely be ashore while you await the opportunity to go back to sea as a Head of Department (HOD).
3. How does promotion work? How do I move up? Can I defer promotion in order to stay in Halifax/Esquimalt/Wherever and not uproot the family repeatedly?
Once you get all the ticks in the box, promotion to Lt(N) is automatic and will come at the appropriate time. It usually coincides with completion of your Board. Promotion to LCdr is on merit and generally won't happen until after you have served a tour as a HOD in a frigate. Some LCdrs return to sea as HODs in destroyers or AORs, but this is by no means universal. Some Lt(N)s never get a HOD tour. Deferring a promotion to stay in a location doesn't work. They will post you anyway. On the bright side, sailors don't move very often. You can pretty much guarantee that you will end up in Ottawa at some point. Over half the Logistics Branch is located there.
4. Is the naval side of log officer in any greater demand than green or blue? Or is it really all the same in the beginning?
Last I checked, it was the Army that had the highest demand. The intake of Naval Logistics Officers is the lowest. The biggest problem we are going to face over the next few years will be the lack of training billets at sea as our Fleet goes in for major refit.
5. How extensive are cross-postings? Might I find myself as a QM at 2 RCR for example as a navy slt?
Cross postings between elements are pretty much non-existent. Although the NCMs are not restricted by uniform (ie you will find leading seamen in service batallions), we don't do this with Log officers. A Naval Log Officer will NEVER be the QM at 2RCR any more than you would find an Air Force Captain as the SYO in a ship.
Having said this, there are purple jobs throughout the entire CF. Postings to CEFCOM, CANSOFCOM and the other dot coms are all possible. Deployments to what one would largely consider army (although really they are "joint") jobs such as Afghanistan and elsewhere are also possible.
Hope this helps.