You don't mention how often you're having flats, but a certain number of them is inevitable. They're just a part of cycling. I've had as many as nine on a century ride, and six on my 25-mile commute (that's uncommon--I ran over a field of broken glass in one case and a pile of thorny branches in the other--but it's just coincidence, not a recurring problem that needs to be addressed). overall, riding in a desert area with many thorns and poor street-sweeping, I probably average one every 75-100 miles.
A few points:
Flats on the front are way better than flats in the rear. I can change a front puncture, including inflation with a frame-fit pump, in less than four minutes. Because of the driveline, rear takes longer.
You can eliminate many of those "hammered-in" punctures by avoiding obvious sharp things in the road and by running your (gloved) hands lightly over the tire when you unavoidably hit some. When you hear the tick-tick-tick of a shard of glass hitting the road, reach back (AHEAD of the brake bridge, not behind it, lest you be sucked in) and let your hand trace the tire as it rotates. usually you'll dislodge the object. Do the same in the front as necessary.
Warning: this takes a little practice. If you're not comfortable, stop and remove the object by hand.
There are many puncture resistant tires, most of them presumably effective to some degree. I don't care much for Armadillos because of the harsh ride, but friends swear by them. Several of my friends also use GatorSkins. I haven't tried Schwalbe because of the weight, though I doubt I'd notice it when i was riding. My favorites for several years have been Panaracer Pasela TG's (TG=Tour Guard, with a kevlar belt. There's also a non-TG model, which lacks the belt).