I've only used Hoppe's bore snakes, but I understand Otis makes good ones too. I use Hoppe's #9 cleaner, but pretty much any gun cleaner will work. There are dozens to choose from.

To clean the breech face and the bolt I use Q tips dipped in Hoppe's, a shop towel, and an old toothbrush. The 15-22 doesn't need much oil. Just a drop on each bolt rail. If you choose CLP for cleaning, you can use it as lubricant as well. If you use another solvent you'll want some oil. Pretty much any brand will do. I have Hoppe's and Otis.

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Or something like that . . .