I haven't had a pinch flat in like 10 years and I was running 700x20C tires back then (when they were popular).

I haven't had a flat in like 15,000 mi, mostly due to Armadillos. With the 'dillos, I don't think any other measures such as Slime or thorn-resistant tubes are necessary. They add very little extra protection and come at a cost, i.e., the messiness of using Slime.

Tire liners will make a regular tire slow and heavy like 'dillos but can chafe tubes and cause flats. An Armadillo tire has its puncture-resistant belt molded into the tire to avoid that problem.

I rode Armadillo Elites for a few thousand miles this season. I took several direct hits from goatheads and never flatted. They aren't as heavy as the regular 'dillos but they are almost as slow. I original got them for Roubaix-style races with lots of dirt roads but they have too much rolling resistance for racing. I wouldn't race on them unless punctures were very likely.