You'll get by far the least flats with the Tannus tires. The 700x23 gives a bit harsh of a ride, and perhaps slightly slower. But... the ultimate in flat protection.

Gator Hardshells have a good reputation for durability, although mixed opinions on the ride. I did manage to damage the sidewall of one, but so far no tread punctures. Still working on trying to wear it out.

The Schwalbe Marathon Plus is a HEAVY tire. Tough, although I do wonder if the thick rubber allows it to get larger cuts than would otherwise happen with a thinner tire. I think their wet traction is somewhat better than many of the treadless tires.

I had pretty good luck with a pair of Origin8 Elimin8ers. A relative cheap tire for having puncture resistance. Somewhat heavy, although lighter than the Marathons. I got about 2000 miles on the pair and thought they were about worn out. But, kept riding them for another 2000 miles or so. I did get a couple of flats, but nothing exceptional.

I do check for the causes of any flat I get, and periodically pick out all the glass from my tires.