According to those currently serving, the most popular watches in the military are G-Shocks. Several have been issued, but I don't know which ones off the top of my head.
As mentioned above, CWC have been issued to the British forces. Precista, too (the older models, not the new ones by Eddie at TZUK). A couple of Seiko chronos were issued to the RAF in the 80s.
The Sinn EZM1was issued to German special forces. Possibly some other models, too.
Some Gallet chronos have been issued to at least one air force.
Going back a bit further, IWC, JLC, Stowa, Laco, and Omega have all been issued at various times.
And then there is what many collectors would consider the grail, the Mil Sub.
So many to choose from... Depending on your budget, you could spend $100 or $100,000. Enjoy the hunt, and post pics of your acquisition!