On the wired side, you do NOT need Cat6 for your setup. I had my house pre-wired with Cat5e between the two floors, and connect my studio router (upstairs), via Cat5e (PC to router, and router to wall (which is Cat5e)) to my cable modem/router (downstairs), which is connected to my ISP at 75MB/sec down, 7.5 MB/sec up. Works fantastic.
The "capability/rating" of internal gear is irrelevant. The fastest actual speeds are governed by your connect rate, which, at a very fast 35 MB/sec, is half the speed I run no problemo, and a tenth the speed I COULD run no problemo, on Cat5e.
If there's no difference in price, put in Cat6. If there is a meaningful difference in cost, save the money.
My $0.02.
And to some I shall not name...worth far less.