I wandered in here to see if you were asking about EA 1 / ISO 597 / 26" x 1 3/8" / S-6 tires, but it's not that.

Panaracer is the biggest name in 27" tires. I wouldn't sweat flats too much to specifically get a puncture-resistant tire; it's an oft repeated phrase that more supple tires are the most cost effective upgrade you can give to any bike. Puncture protection belts tend to make the casing stiffer and impair the tires' ability to act as your suspension.

I carry levers, a wrench for axle nuts on bikes that use them, a small patch kit, and a pump or CO2 inflator (strongly prefer the pump). Most roadside flats I've had to fix were due to old rim tape, not road debris, but YMMV. I'd suggest you invest in new rim tape when you have the tires off to replace them, and save yourself a potential hassle later.