Welcome to the forum. If you have access to CCI AR Tactical, it too is good ammunition and runs cleaner than most. CCI Ammunition - Product Detail

No need to be concerned with the exterior of the barrel unless something crazy happens. If your OCD insists on addressing the barrel, you could use a CLP spray through the handguards and let it drip dry.

I run everything wet to include my 15-22. Not dripping, stupid wet but wet. Firearms aren't all that picky about lubes. I personally grab whatever's in reach which is normally a synthetic motor oil. Just clean it now and then, lube it, and fire away.

Try to keep the lube away from your ammunition, magazine interior. If running several magazines over the course of a single session, I'll put a few drops of oil on the bolt to keep it a little wet.