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ja1124 check out Panaracer's Pasela tires. They come in 700x35 and a number of other sizes. They are a good option if you prefer a supple/flexible tire that is also versatile. They roll easily and respond well to air pressure tuning while also being durable in average conditions. They've got enough extra grip to help in edge cases but not enough to slow you down in most conditions. Wire bead variant is typically around $25 and some times lower. Folding bead is lighter and not much more expensive but may be a little harder to find.
One of the main benefits of the Pasela is it's light and flexible casing but that could also be a limitation if you ride in thorns, glass and other sharp objects regularly. I've never had flat problems with a set of Pasela tires but could see running something with thicker sidewalls, more protection and/or tubeless if puncture flats were a regular risk on my rides. The Pasela is capable of gravel and off-road riding in my experience and I've done plenty of both on them without issue.