The first stat I look at for hitters is wrc+, because of how it is normalized, a good summary of total hitting ability, and the fact that I usually go to Fangraphs for stats and that is the normalized stat they show. If I went to bbref, I'd probably be pretty happy with OPS+, and for less stat inclined people that would be a lot easier to explain. The two lineup pretty closely most of the time, so it doesn't bother me if people use one or the other. It's easier to use a normalized stat than trying to figure out what the average OPS is now or was 20 years ago. You can compare players across eras more easily. And you can avoid applying standards that might have been true when you were first paying attention to them, but are now completely different.Not to sound flippant, but to return to basic principles, I think the average person is looking for a measure of how well a guy is performing.
In Ye Olden Days, BA was pretty simple in that regard - .200 is the Mendoza Line and .300 plus is All Starish. I remember when I first came across OPS - I thought "cool - but I have no emotional understanding of what these numbers mean, the way I do for a guy hitting .340. I still feel that way occasionally, when running into something like "Dude, the guy's FARKIFIPFSH is 1.456!"
For pitchers I like K%,BB%, and xFIP. If xFIP- was on the first page of Fangraph stats I'd probably look at that. The rate stats are pretty predictive of success at pitching. And xFIP helps to cut through the short term luck when it comes to small sample size pitching numbers. Some players do have long term variances between ERA and xFIP, but that's why I look at the player's past history to see if they have that in past.