I built a 13'x13' 25° climbing wall with 2"x4" on 16" centers and its very stable, very little flex, however 2"x6" will practically eliminate that tiny bit of flex. I think a 2"x8" is over kill
I used 2X6 at 24 on center, I just put horizontal supports in ( not even sure if necessary) at 3 foot intervals. I feel it did help with the ply-wood not flexing when climbing on it. But 16 on center should be fine with 2X6's.
Personally I'd go with 2x6 material w/ 16" spacing. I'm really happy the way my wall turned out, the thing is totally solid. Run a line of liquid nail on the 2x before you put up your plywood to minimize any flex or creaking.
On another note, if you can spring for the higher grade plywood, go for it! My wall has the midrange quality plywood and there are definitely a splinter factor to lookout for. Not a huge deal, but that's one thing I would do differently next time.
I have a wall that is nearly identical to your specs. I framed it with 2x6's on 16" centers. It is very solid. The 2x8's would be overkill. Good luck with your build.
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