Every company has different definitions for "medium" and "high". Fortunately, Midway recognizes this and has measured the height of every ring they sell. They measure from the top of the rail to the bottom of the scope, and using this measurement I've found scoped AR's to work the best with a rings that are .75-1.0", this gives an scope centerline of 1.25-1.5" above the top of the rail.
Instead of worrying about getting the objective as low as possible, place the scope so you get a good sight picture. Shoulder the rifle with your eyes closed, then open your eyes. You shouldn't have to move your head to see through the scope.
I have two AR's that have both free float tubes and scopes. One has .75" high rings, 44mm objective, and has has about 3/8" between the objective and tube. The other has .65" high rings, a 32mm objective, and has 9/16" clearance between the objective and tube and I've got new rings ordered since I have to squish my head down on the stock to get a good sight picture.