It is absolutely possible to manage park remotely. I was in the Army 7 years and definitely understand how hectic it can be with the moving/deployments. To answer your question more in depth, it really depends on what type of park you buy. If you get a park that has a lot of issues/POHs, then you'll certainly need to be more involved/probably pay the manager more.
I bought a turnkey park and my part time manager probably does around 1-2 hours of work per month for me and I do maybe 2 hours of work a month. I love this setup and the upside for me was that the lot rents were significantly below market.
As far as finding a manager, as soon as I purchased the park I sent letters to every resident letting them know of new ownership as well as rent increase. I made a note in the letter that I would be looking for a part time resident-manager and had about 4 calls. I conducted the interview over the phone and did the background check online.
It can definitely be scary at first but if someone doesn't pay then immediately send the 3/5/10 day notice and that will usually get them to pay quick. Good luck to you.