Since your max range is 200 or less, you shouldn't have to spend a great deal of money to obtain decent optics and mount. Consequently there are a ton of good options. You shouldn't need anything bigger than a 2-7 or 3-9. Some would even suggest something like a 1X prism red dot along the lines of a Vortex Spitfire with a DRT reticle for no more than 200 yards. There's a lot of preference and variables here.
On a mount I'd suggest something along the lines of a one-piece cantilever design like a Burris PEPR. With an AR you need a slightly more specialized mount than what most bolt rifles use. Still, even here there are preferences and variables all over the place. These slightly more robust mounts like a Burris PEPR and such are probably a better match for the harsher recoiling of a bigger caliber AR.
I have one Armalite .308 AR10 with a 20" barrel that I have a 5-20 Burris scope attached on a PEPR mount and a 16" model with a Burris 2-7 on a PEPR mount. I found the Burris 2-7 E1 scope on sale for about $135 last year and the mount was on sale for $75. I could see myself also going with a 1X prism red dot on the 16" carbine since I have the longer 20" AR, but if the 16" was my only AR10 I'd probably stay with the 2-7 scope for a wider use.
Again, there are lots of options, preferences, and variables, and yours could change once you really start to use the rifle for whatever uses become your priority.