A general wipe off and/or wash with water and re-lube should be fine. Though I subscribe to not cleaning every ride unless it really needs it. Less full on cleaning the longer things last I find (wipe down and lube is fine).
The chain checker... is that the latest Park Tools one? I've noticed they've change the wear indicator. Used to be .75% for replace chain and 1% for chain & cassette but now it's .5% and .75%
I'm convinced they've got some deal with the chain & cassette manufacturers going
Another verification on the wear is to get the chain on big & big rings, and try to pull the chain away from the side of the front chainring where it's tightest. It should have a slight give but not pull away with a gap.
One thing I've found though, if I've decided to replace the chain, I replace the cassette no matter what as a new chain just slips on an old cassette even if it doesn't seem that worn. But my chains last for 1000s of miles.