On a BR rifle, most shooters use Davidson/Kelbly style bases. There are others now making this same type of base but all that I have seen over the years are similar, if not the same, in height. If you meant rings, any standard height ring that is made for these bases will work. The companies that make the rings for BR rifles know what heights are required to mount the scopes. I prefer high Kelbly rings personally to keep my face away from the stock as much as I can.
The factory lens covers are still with the scope. I never had a need to buy leather covers.
Peter