My daughter-in-laws brother just came back 3 weeks ago and he's also single. (He's also a member of special forces.) After considering all his options, we booked him on the Oasis of the Seas and he absolutely loved it! Said it was a great way to relax, party, enjoy the nightlife, meet the ladies, and had lots to do. We've been on the Allure of the Seas and one good thing about those ultra-mega ships, they carry alot of people (upwards of 6000 passengers), so it obviously increases your chances for meeting people.
If you want to try NCL, take a look at the new Breakaway.
But don't discount Carnival - their newer ships are nice and they do tend to attract a younger crowd and lots of singles.
And lastly, you might also want to consider Princess - a bit more of an upscale crowd from the other three, so it's very nice.
And from a Vietnam vet to an Afghan vet - thank you for your service, brother!