@Curtis Lipsey
I'm far from an expert and can't answer your question directly... however my limited experience might be useful to help you think from a slightly different perspective... alternately you might get inspired.
I retired from the AF a couple years ago... and purchased a house at every stateside assignment. Becoming a long distance landlord four times over.
1) First, I'm led to believe that "lucked out" that I only had four stateside assignments. Apparently you can't get a 5th conventional mortgage.
2) If you buy were you are stationed you might have the added benefit of being able to buy with conventional (and possibly even VA loans). If you purchase with the intent of making it a rental you can "do all the same research" for rentability with the added benefit of being local. You can develop a rolodex of craftsmen (painter, plumber, carpenter, handyman, etc) and find your property management company (if you want one) while you are still local.
Note: I've bought 4 houses and never once did this... I was always too focused on work... but if you're lucky maybe between you and your spouse you would have the available bandwidth to do it.
3) if you purchase in NM you might benefit from the benefits of a NM LLC...
4) Buying where you live (or at your next pcs) with the intent to leverage it's sale with a 1031 swap for a new investment property (potentially this time in Kentucky(?)) later.
5) If I had to to it all over again I wish I had done 1031 exchanges with each of my properties into a rental/development in Austin such that I would own 4 houses in Austin in 2021... with a single property manager etc. Hmm, maybe I should look into that NOW. Lol. I Just had that thought as i was writing this answer.
6) I ended up (currently) with 4 different property managers. Tl;dr: put as much effort as you can into choosing your management company...
A) First one was terrible, but I didn't know it until I had my first "problem tenant" after almost 15 years.
B) Second property manager was a part timer, friend of a friend, and I was trying to save money. Mistake!
C) Third property manager I put quite a bit of effort in finding. Worked out great until she retired after almost a decade. She sold her business to an associate and it's been great for a couple of years.
D) Fourth manager has been acceptable to good for the last 6 years... with no real complaints... partly because I did a lot of research and partly because I haven't yet had a problem tenant yet to test them.
E) Fifth manager is the new management for the first house... who is by the way the second replacement for that house. The first replacement I interviewed and hired to manage the property, including make the property rentable after the problem tenant "destroyed" it. After two months I ended up firing her, fixing the place myself (I mean hiring contractors etc myself) and hiring yet another management company (third for this propert). Honestly, I'm unconvinced that the current manager is much better than the first... beggers sometimes have to compromise... we shall see.
F) My last property manager is also problematic. I interviewed over 5 companies and really thought I'd done my due diligence (I've got non-trivial experience now afterall) and had a list of probably 25 questions that I asked each prospective manager... Well, in my opinion the guy is an excellent salesman (could sell ice water to an eskimo) and even an adequate businessman... however his parter/daily manager is a pampas ***. He is insulting, does what I consider to be the absolute minimum, and ... well, I'm firing them as soon as I can replace them without a significant "early termination penalty."