Hi Mike,
Welcome aboard. Your question about cleaning is a good one. I can answer it in two parts.
First, cleaning requires tools. There are various tools out there. Being an idiot, I own a few cleaning tools. A thread on that is here:
http://smith-wessonforum.com/smith-w...use-clean.html
As far as cleaning solutions, I always advocate the good old standby's. Hoppes No.9 solvent for cleaning off carbon fouling from the bore and bolt carrier group. Hoppes Copper Solvent for removing copper fouling from the barrel (when needed). With these two solvents, I can give my AR15's a good cleaning.
There are some cleaning products that are worthwhile. Some save time.
Hoppes Elite Gun Cleaner: I buy this in a big spray bottle. It works well. Doesn't cut carbon & fouling as quick as Hoppes No.9. It is polymer safe. I don't worry about discoloring or ruining polymer parts.
Breakfree CLP: A great standby. Cleans, lubes, protects all in one shot.
Ballistol: My current all-round favorite product. It's a non-toxic clean/lube/protect product. The more you use it, the easier subsequent cleanings become.
Regarding brake cleaner...
If you decide to use brake cleaner, make sure to buy non-chlorinated brake cleaner. The chlorinated stuff will damage polymer & rubber, and may affect your firearm's finish. Even with non-chlorinated, test it on an inconspicuous area of your rifle to see if there are any adverse reactions. Non chlorinated brake cleaner is an excellent degreaser.
The only time I've used non-chlorinated brake cleaner on my AR, was to flush out my gas tube. I only do this when I think (most of the time incorrectly) that something might be fouling my gas tube. It's irrational. In truth the hot propellant gasses burn off any fouling in the gas tube.
I guess you can use non-chlorinated brake cleaner to flush out a lower, but I've never had to do that either. The lower doesn't get dirty.
Again, congrats on your new rifle. All of what I say above is personal opinion, not absolute truth. I wish you happy & safe shooting!
Happy New Year!