I have Warne QR rings on a couple scopes for a competition AR, one 1" and one 30mm. They go back on without having to re-zero, but I check anyway, just to be sure. Cabela's has them at $59 but I do not remember them being that much, so shop around.
The height depends on the scope bell size and the mount on the AR. Going straight onto the flat top receiver, you probably need high rings. Tricky part is getting the scope far enough forward. Usually that would mean some extension like LaRue but that is way over your budget.
Lee
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