get a vudoo bore guide, cheap enough and fits perfect
check the size of the rod, not all 22lr rods are the same diameter
i use a push through jag (i use wrap jags on my center fire) because im not cleaning down to the steel on my 22
i use bronze brushes, just never got into the nylon ones but i dont brush often
most often i use hopps on a few patches followed by a dry
if i have time or put a ton of rounds through it ill do a few strokes of a wet brush, then push a few patchs through