Which puncture-resistant tires? I commute on city streets and have had two punctures in 5 months: first a roofing nail, second a small shard of glass.

Punctures are a nuisance.

I've read some people recommend Schwalbe "Marathon" tires. A comment in reply to Are slick tires worth it for commuting? also mentions "Conti Gatorskins, Specialized Armadillos, Soma Everwears, et al."

Is there anything to distinguish one from the other? For example if an LBS stocks Conti Gatorskins should I say, "No, I'm looking for Marathons"? Or are they more or less equally effective (price and, more importantly but less easy to measure, puncture resistance and rolling resistance)?

My wheels are 700x32.
The Schwalbe Marathon Plus (not just the Marathon) is widely regarded as the most flat-proof tire out there. It's also heavy and expensive, but if your priority is avoiding punctures, I don't think it can be beaten. ISTR reading about a round-the-world rider completing 50,000 miles on a pair without a flat.

Specialized Armadillos are not, in my experience, particularly flat-resistant, although there might be a beefier version than the one I was riding on. I have no experience with the Gatorskins.

Anyhow, there are definitely differences between flat-resistant tires. There are even differences between Schwalbe Marathons variants.