Think it depends on the pub too - for instance we play one that has an older, more sitting and watching type rock crowd (a lot of them really know their stuff musically and always have a chat after the gig) so for them we do a mostly rocky set but still throw in newer stuff (they like a bit of Muse and recently loved a Ghost track we do, though had no idea what it was!) In the same town we also play a more 'town centre' type pub with a mixed age dancy/jump around crowd, there we stick more poppy stuff in. Newish material that goes well are our rocky versions of pop songs by The Weeknd, Ed Sheeran, Coldplay and a mash up of Cake by the Ocean (newish) and Teen Spirit (old).
We often play some Biffy Clyro, Royal Blood and Blackstone Cherry too
In both a good smattering of well known classics is needed and you do need a few cheesy trigger tracks.
What surprises me is that my daughters (15 and 12) often know the older songs, almost like they absorb big well known tracks from the ether.
I have always detested Sex On Fire but we had to learn it for a wedding gig as a special request - the rest of the guys suggested we play it at a gig which I reluctantly did. Fortunately the punters looked as bored by it as I am, so it's not been mentioned again!
I'd say just pick really good songs that you can all play well and have fun with and try not to fall too deep into the "Same songs, different faces" bracket that one landlord once described some other cover bands to me as. Stick a few brave choices in too as they seem to be the ones that the regular gig goers will remember and ask you about.