Wichita resident here.
Just wanted to say, regarding homes with acreage, that's a pretty tough market for buyers right now! We just closed on a new home this weekend. Our agent was talking with the sellers (who wanted land in the country) about how hard it is to find anything. A home with any real land will go in seconds, if not even before it's listed. The sellers were able to find a place with a good amount of land, but it is quite a ways from Wichita and they just happened to find someone who was about to list theirs...it didn't even hit the market. From hearing all of their conversation, just be ready to offer full price, if not even several thousand over asking!
We love Wichita and have lived here for about 11-12 years. I, too, enjoy a lot of the activities you listed. We have a couple of kayaks and enjoy getting out on the water. There are a couple of large reservoirs within about 45 minutes, and several smaller lakes that are great for kayaking, fishing, and camping. There are a lot of nice gun shops/ranges in town. Kansas is a very gun-friendly state. We now have Constitutional Carry, and NFA stuff is good-to-go.
As for places to start looking, you might focus on some of the smaller communities in the surrounding area that could potentially have some land... Goddard, Haysville, Kechi, Valley Center to name a few. If you need a Buyer's Agent, let me know if you'd like the name of the lady who worked for us. She's gotta be in her 60s and has been doing this for years...I swear that lady never sleeps! She would send emails/texts late at night and early morning (never woke me) with updates, etc. She was very on the ball for us.
Good luck!
(Oh yeah, can't speak to any military stuff, but I'm sure someone will chime in.)