I learned about this the hard way a few years ago, so:
First......should I use some sort of fuel stabilizer in the gas?
I would unless you plan on starting it up every so often.
Second.....I'm going to change the oil and I could get the oil at the dealer (and they will tell me I need a certain brand I'm sure) but what do you guys recommend. Also.....If I put in fresh oil now am I to assume it will still be perfectly fine in the spring to ride with that oil into the summer?
Get what is recommended. I believe that as long as the temps stay pretty even (no condensation) there is no issue with using the oil to start the season.
Third......Sounds like putting oil in the cylinders is out of the question due to limited access?
You really can't reach the spark plugs to remove them? I have sprayed WD40 in the intake while tuning it over with the starter, plug wires off of course.
I'll take out the battery and charge.......any other tips?
Get one of those foam knee pads that gardeners use to set the battery on. If it sets on concrete it does hurt the charge.
I used to just park toys for the winter and then fought them in the spring; not any more! I either set it up on blocks to help the tires or take it around the block every time the sun shines enough to clear the snow off the street. Of course in your neck of the woods that might not be too often.