Well, a 40mm scope should fit on top of an M14 with no problem using Med height rings.
Not sure how high the Arm 18 is specifically, but I currently use low rings on my machine with no clearance problems. My scope mount hovers over the receiver high enough.
The arms mount seems considerably lower then mine, so medium might be the trick unless someone chimes in that you need higher.
I like to have my scope as low as possible and would recommend the same.
The comb on the M14 is ergonomic to the iron sights, and a scope can feel a bit high.
Most scopes use 1" rings unless otherwise noted and it's not otherwise noted on the Bushnell website. I would measure it . . . you must have a ruler around somewhere ?
Another thing you want to worry about is the quality of ring. You need something heavy duty, with perhaps 4 bolts per ring instead of 2. The recoil of that rifle is going drift the scope after several firings with a 2 hole ring. Some rings are 30mm with 1" spacers, I would avoid those.
A nice set of weaver 6 hole tactical rings is what I recommend.
You're just going to have to go ahead and buy the base you want, then do some measurements to get an idea of the minimum clearance you need.