I have a couple carbine courses under my belt. Run whatever rifle you want, AR would be a good choice as that is what most will be running. Run whatever length you want, just know that if you are running a brake, the people beside you will not be your friend anymore 5 minutes into the course. Run a blast shield. Short or long doesn't matter. On the courses Ive been to people ran all different length, as long as its reliable and sighted in not much else really matters, but again, brakes do piss people all, and if you do any positional shooting such as supine, the blast won't feel too great on the legs. I ran a 14.5, we had all different lengths from 10-20in barrels, use what you have, at the ranges you will be shooting, a longer barrel will give you no better accuracy not to mention is heavier and longer so the ease of moving it will decrease the longer it is. This is not benched shooting so be aware of that.
As far as kit, run what you are comfortable with, Ive run plate carrier or belt rig. Personally, i would go with a belt rig as it is more comfortable. you should only need 3 mags, so 1 in the gun, 2 on the rig. no less, more if you really want but most courses of fire are for 3 mags. For holsters, whichever you prefer, drop leg or belt, your preference, I run both depending on if I am running a carrier or not. Just make sure ahead of time that it fits the requirements, many courses do not allow Serpa's unless it is job issued, ie: you are a police officer.
Is this the CSC Carbine 1 course? if it is, talk to Carl the instruction before hand and he will get you sorted.