A few things to consider:
The rack itself needs to be either attached to studs or screwed into something else that is attached to studs. Since it is unlikely that you would be able to get enough screws into studs by positioning the rack "just right", the usual method is to cut a sheet of plywood to be a little larger than the rack and all other equipment and mount that to the studs. Then you can put screws through every mounting hole of the rack into the plywood and it will be very secure.
You are planning on 4 receptacles. Most typical installations I have worked with, whether computer, video or telephone equipment (or often a combination) only end up using one or two receptacles (so a standard duplex will be fine) and plug surge protectors into each receptacle. That allows for easy on/off without unplugging (and unplugging is a pain to do reaching past all the equipment into the back of the rack) and provides some protection against surges. If you have high power requirements (as opposed to just a lot of different small items, which is the more common situation) then whether a duplex or a quad you can bring in either two circuits or an MWBC (two circuits in one, essentially). If your expect power needs are 1500W or less than one circuit is plenty.
Note that four receptacles on one circuit costs very little more than two receptacles, just may not gain you anything at all.
There are three ways you could go here.
- Standard wall receptacles. Install an ordinary one gang (2 receptacle) or two gang (4 receptacle) box in the wall. Run the cable. Install the receptacles. Put on an ordinary cover. When you are ready to put up the plywood, measure where the receptacle is and cut a rectangle where the receptacles will be. Leave an inch or so all around the cover plate so that you have a little work room in case so the receptacles can be replaced without taking down the rack and the plywood.
- Make the Plywood the Wall. Cut a hole the exact size of the needed opening (one gang or two gang) in the plywood. Install the plywood. Cut into the drywall through the hole in the plywood. Install the box and receptacles such that the front of the box/receptacles is flush mount with the plywood - i.e., the plywood becomes the wall.
- Surface Mount. Install the plywood. Install a metal box for the receptacles. Run the cable down the wall/plywood and into the top of the box. Install the receptacles. I don't think the cable needs damage protection on the wall in this case, but if it does (the pros will speak up if it does...) then use conduit or wiremold for the few feet from the ceiling to the box.