First off I'm new to the site and love it. I have been reading posts for a few weeks now and have learned valuable info. I have a RRA tactical  Car A -4 with the detachable carry handle and was wondering if I need Medium or High see through rings. I recently purchased A Nikon pro Staff       3 x 9 - 40??

Welcome; lurking and searching are your two best friends.

Generally speaking, the closer the optic is mounted to the bore, the better.....not only ballistically speaking, but also for ergonomics [cheekweld], particularly on the AR platform.  You have a flatop, good start.

Any mount that would allow you to see the irons through it would be ridiculously tall.

If you are wanting the flexibility of using the magnified optic or the BUIS, then a throw lever mount may be a good choice.  ARMS and Larue are the two most respected manufacturers of same, with Larue's SPR mount being a particulary good design providing more eye relief flexibility.

I am not known as a Larue cheerleader, but I do really like my SPR, in addition to the several ARMS products I own.  

You may also want to consider a flip-up rear sight such as Troy or ARMS #40L; both should be low enough with most optics mounts that will support a 40mm objective.  

As always, try to test fit if at all possible before buying, or solicit input on the exact combination you are interested in, once you decide what it is.

  This is my Monarch UCC 3-9x40 in ARMS # 22H (High) rings. For me, this is the right height and will give plenty of room for a BUIS if so desired.  These rings can be had for 80-100 bux on the EE and sometimes come with the 30mm to 1" reducers .  Happy hunting and enjoy your rifle and Nikon, best bang for your buck as far as I am concerned !