When it comes to a new firearm, be it handgun or long gun, I do an inspection of them prior to shooting them, but don't waste time cleaning them prior to firing. Some are gonna flame me for stating this, but so be it.
I use both a brass wire brush and a cleaning patch. Using one doesn't mean you don't have to use the other.
Cleaning an AR-15 means breaking down the bolt to it's various parts and cleaning both exterior and interior surfaces. Clean the bore and chamber well. Lightly lube the bolt and it's parts prior to re-insertion into the receiver. Insure that dirt, debris, etc. are cleared out and away from the trigger group / housing.
I use Hoppe's #9 and Rem Oil. Tooth brushes, cotton swabs and plenty of bore patches are essential to a good cleaning kit.
I'm sure that I've forgotten some things, but there will be others to come along and fill in the blanks.