Two options here: 700x41, and 26x1.75.

The Marathon is Schwalbe's most famous, standard tire. It specializes in nothing, but is good for everything, and is super tough because it's stout.

If you truly don't want tire problems and you're sane or willing or realistic enough to know that with weight comes good things, but you don't want to go overboard with the SmartGuard liners Schwalbe puts in its ultrastoutest tires, then the Marathons are the tire to beat.

The one we sell as a 700x41 is the one Schwalbe calls a 700x47.  The 41 measurement is when it's mounted on a 22mm wide rim; it'll be a little less if you use 20mm rims.  It will fit most 700c bike we've ever made, and ought to fit any bike billed by others as a touring bike; and is a good choice for tandems, too, which is why I put it on mine.

It weighs 861g, it is German Stout, but every gram pays its way by providing longer wearing tread, tougher sidewalls, and extra puncture resistance. If and when you get past the weight demon and are just out for supreme reliability and great all-around rough stuff performance and all that, get this tire. Make sure your bike has room for it. Inflated (as you'd ride it), it stands 708mm tall. Compare that to what you're on now, and see if the clearance can swallow up a radius of 354mm.
To measure your current tire, set it up dead vertical and measure from the hub center to the floor.

You'll probably get 7,000 to 10,000 miles out of it. That's a prediction, not a guarantee, but it's conservative. Wire bead.

The 26x1.75 is its 26-inch equivalent.