From one old 'Tropic Lightning' troop to another, thanks for your service and enjoy shooting your recurve. Give some wood shafts a try; good ones shoot as well as aluminum, and smell a whole lot better!
I don't know much about three under, but I have always shot with a glove; others swear by tabs. That is probably more of a personal choice, so you might try both and see what suits you. The only time I use an armguard is when I have on heavy clothing that would interfere with the string, but I shoot a longbow, so my grip will be different from yours with a recurve.
Again, a sincere thank you for serving in this dangerous time in our history.