I use any non-Teflon containing oil. Right now I'm using a spray can of 'Blaster' PB50 All-Purpose Lubricant from Home Depot. Regular old 3-in-1 oil or any of the equivalents work fine for protecting bores and outside surfaces. I'm not picky about it.
As for how light, I put just enough so that all of the patch is lightly dampened and it just barely feels oily. If I happen to put too much, I roll it up in a ball and squeeze it in my fingers as hard as I can to get the excess out.