I find that the old chain and cassette skipping due to wear is not as common as skipping after installing a NEW chain on an OLD cassette. So even if you changed out a chain before skipping started with it, you may be surprised to find that you can't use the new one until you also get a new cassette. Occasional measurement is much more reliable for sussing out a worn chain than going by mileage. Despite its well documented shortcomings the Park Chain Wear Indicator, Chain Wear Indicator - Park Tool, is a useful little tool that does the job, albeit a bit conservatively.

I use SRAM Red cassettes which are very pricey, so it is worthwhile to me to waste a few miles of chain life in order to protect the cassette. For that reason I go by the lower wear indicator on the Park tool when checking chain wear.