Tack cloth?

I personally hit my parts with a quick blast from a canned air duster right before painting.  For me, tack cloths have had a habit of depositing more gunk than they remove, and they also make it really easy to break things off your model.

I use paper towel wet with liquid that depends on the paint.  I use paint thinner for oils, alcohol (56%) for acrylics.  Not too wet- not dripping, but damp.  I used to use Kleenex but found it leaves lint, which the paper towels I use do not.