quick note on maintenece f your bore snake. An easy way to clean it it to put it in a sock, tie off the end of the sock in a knot, and throw it in the washing maching.

as far as a good cleaning kit. Spend the little bit extra and buy a 1 piece, composite cleaning rod. If the rifle is a bolt action, get a bore guide too. Jus t acouple dollars. the 1 peice rod saves scratches on the barrel where a segmented metal rod can unscrew and do the damage. The bore guide just keeps the rod straight down the barrel, also helping protect it from un-needed wear and tear.