For field cleaning, I use the Otis M16 buttstock kit. It has everythiong you need for when you're on a hunting trip or out camping for a few days and you don't want to carry a lot of extra stuff around.
For bench work, I use Dewey and Boretech coated rods with Shooter's Choice solvent for the bore and chamber and Breakfree CLP for everything else. I use Parker-Hale style wrap-around jags because for me, they help keep the patch from getting stuck in the barrel.
Does your 4-piece kit have a T-handle? If so, you can use it for the chamber brush. I avoid sectional rods for the barrel because they can scratch the bore. If you don't have a T-handle, buy a handgun rod and use it for the chamber brush.
Don't overclean because it can cause more damage than good.
I assume you know how to break-in the barrel. If not, find out how to do it here.