Here is a detailed report on the military advertising budget - it's from 2003, but it gives you a starting point:
In brief, according to this report: "DOD’s total advertising funding increased 98 percent in
constant dollars from fiscal year 1998 through fiscal year 2003—from $299
million to $592 million. The advertising cost per enlisted recruit has nearly
tripled and is now almost $1,900."
Minnesota Representative Betty Collum released an interesting press release about the NASCAR marketing. The release points out that while the Army and National Guard sponsor NASCAR teams, the Marines, Navy, and Coast Guard have eliminated their sponshorships.
Also, the great War Resisters pie chart depicting the percentage of the federal budget devoted to military spending (not specific to marketing, but a wonderful and eye-opening resource): http://www.warresisters.org/sites/default/files/FY2012piechart-color.pdf
Hope this helps you get started!