How should I prepare a log home for vinyl siding?
Your first question is a bit unclear, but I'd consider installing blocking to bring the wall on plane, then OSB or plywood sheathing. You could have a selection of spacer blocks on hand and pull lines to check the needed thickness at each vertical on 24" centers. I'd probably pull horizontal lines top and bottom, then pull between them as you install the blocks. 

Installing just furring strips will leave you with a wavy wall unless you also do the varying-thickness blocking. Sheathing would cost roughly the same anyway and give your siding better support.

You should have housewrap (a drain plane) behind the siding. This is not a vapor barrier and will allow the wall to breathe. Almost no one installs poly sheeting, for example, behind siding.