I did not even think about military! We have a base about 30 minutes away.
I also did not think about yard maintenance. The yard (grass area) is small, there is a large patio off of a deck and a few landscaped areas. I think it could easily be managed with about an hour of work a week.
How does choosing a tenant work? Can we just choose whoever we want or are there discrimination concerns?
Study your state's Uniform Owner-Resident Relations Act. Everything you know is in there. In fact I recommend memorizing it not word for word but well enough to be able to answer the question "is X legal in my state" without having to look it up.
Since you're not sharing accommodations with this tenant, you may not discriminate based on age, gender, disability, religion, ethnicity, or anything else that would be forbidden if you were, say, interviewing people for a job. You may, however, discriminate based on income, criminal record, and rental history. With a military officer as a tenant, income and criminal record won't be a concern and your background check process may get a lot easier.
You can improve your odds of getting a military tenant by putting your advertising where they are likely to see it. Advertise in the base newspaper, and if you make use of an online classified ad, use military-friendly language. Including the words "military" and "family" would be wise. Emphasize the upscale ambience, the suitability for entertaining, and the presence of a small yard and patio area. Mention the number of rooms and the approximate location and square footage. Also mention your monthly rent and damage deposit.
Advertising a space for rent is like fishing (minus the negative experience for the fish). You bait your hook, you drop it in the water, and you wait for a nibble. When someone calls you to ask about the property, that's your nibble. It's the point at which you and the tenant start screening each other to make sure you want to continue in the business transaction.
Find out about your caller by chatting freely, and answer all his or her questions. Find out if they have pets, how long they plan to be in town, and when they expect to move into whatever space they want to rent. Get information about occupation and income (the officer's rank is the information you need; look up the relevant salary because it's public information). At some point, invite the prospective resident to come by, see the property, and talk about lease qualification which depends on sufficient income and a positive credit, criminal background, and rental history check. If you hear a "no thanks", then what you have is a misalignment of interests, and your property doesn't match that particular renter's needs. It's nothing personal.
When you meet, exchange ID and make sure the person you're talking to is who they say they are. If the tenants have provided you with references, you should have done your homework. Collect consent for a background check on all adults who will be living there if you haven't done it already. Have your lease on hand and be prepared to explain it clause by clause, but don't sign a lease until you get a thumbs up from the credit and background check and have called and verified each reference. Make sure you know the names and ages of everyone who will be living there. This is also how you establish yourself as someone who is proactive, savvy, and ethical enough to correctly hold up your end of whatever deal you make. Also, if you're trying to attract a military renter, the place should be immaculate.