Working with the military is a tricky business. It can be done however. Depending on how you plan on distributing the final product (web, DVD, etc.) and what your 'idea' entails will be the main obstacles for getting this thing greenlighted. Bottom line is the services want to look good and anything portrayed by active personnel will have to be closely scrutinized by the Commanding Officer (CO), the Public Affairs Officer (PAO) and a host of individuals you couldn't anticipate having input. All this is because the services also have to cover their butts. Well established careers have been wiped out for less than what you are innocently describing because of real or perceived improprieties arising from an unsolicited production. For you it's 'hey let's make a movie', but for the military your idea may potentially be something a lot of folks may get burned on.
To alleviate the 'sweat factor' for your initial contact (Col. 'X') the best course of action is to have a well written premise / treatment and basic production proposal all neatly put together to present for the Col.'s to review. Though you say you don't want to make this 'too complicated', remember that the military has a resevoir full of regulations regarding media they have to follow and therefore do not have the same freedom and 'spontaneous brushstrokes' you have as a civilian. If the Col. likes your P&T and proposal (remember, the less the service has to provide, the better your chances and don't ask them to pay for anything. Period.) and it passes a basic review, then when you write the script keep him/her and 'his' people involved in the process much as possible. Though it may seem to take away some of your creative freedom, again remember that resevoir of rules they have to deal with and that you want to utilize 'their stuff' and personnel in your flick. More often than not, you'll come up with something better than you thought because of their input and it will smooth the process because they will feel secure with the content. Be advised, their interests will be dominant in the project but you would go through the same thing dealing with big investors or a major filmstudio anyway (remember, you're using their stuff.) Also, the most likely will want to have control over the project rights or at least the right to distribute it amongst their service as they see fit. Offer the second one to them up front and they may not push for the first.
Lastly, if they do greenlight you during production follow their rules. It may seem constricting but you'll be surprised how much extra stuff they'll give if you ask for it. When they say no on something, leave it at that. Also, be very clear and organized with your production schedule and the resources/personnel required for a day's shoot. Be punctual (early wouldn't kill you), do the work quickly and efficiently as possible and get out so you don't wear out your welcome. Make sure they see 'dailys' in what's called a 'prime cuts' tape or DVD with the best cuts of the day and keep it short (10 minutes tops.) You will find that once you have their trust and they are comfortable with your work style (the closer to theirs, the better) the more they will do to facilitate the project. Once you get it in the can, keep them in the loop during the edit (since they'll have to approve the final product anyway.) This will keep up the trust level and make it easier to do future projects. Get the edit done in a timely fashion and screen the final cut with the Col. and his people to get final approval. When they give you the thumbs up, you're off to the races. If for some reason they want minor changes, make 'em. Because you kept them in the loop, they will most likely be satisfied with what you put together. Just remember; all the rules of copyright still apply! If they want to add copyrighted music images etc. that either is not owned by the DoD (Department of Defense) they'll have to get the rights to use said material. In fact, it wouldn't hurt to have a basic 'plain english' aggreement written up just in case... but that definitely leads to 'complicated'....
