I find Pirelli Cinturato Velos offer a very good overall compromise. Puncture resistance is excellent (far higher than any of the race tyres and even rated higher than Gatorskins). Grip is excellent in wet or dry. Rolling resistance is very respectable and hard to tell any real-world difference in speed from the race options, especially on rougher road surfaces. I run these tubeless, but they can be run tubed-too if you prefer.
I also have the latest and greatest Conti GP5000S TR on my other bike and while I really like them and objective tests suggest they should be faster, I don't really notice much of a difference out on the road. They do feel a little more supple, but that's about all. I haven't punctured on them either, but only covered just over 1000 km so far.
I think either of these tyres would feel like a big step up from Gatorskins.
https://www.bicyclerollingresistance...rato-velo-2018