For a screw that looks like it's going to be a problem to remove and the head is deteriorated or is otherwise in less than good condition, try dipping the end of the screwdriver in a little valve grinding compound. Sounds weird, but the compound goes along way toward stopping the slipping of the...
I must be a clean freak to some extent. I rinse my used funnels out with gas and then dry them off and out, then store them up side down on a dish towel that I stole from work. Also I stuff a paper towel in the neck to keep out grit, and absorb any wet residue.