Your Giant Escape 3 came with 32mm tires, and V-brakes. (Road bikes with caliper brakes are often limited to about 28mm tires, since there's not enough clearance under the brakes or at the frame.)

You might be able to fit 35mm tires. The wider tires would be nice on the canal trail, which riders say isn't as good a surface as the compacted crushed stone on the GAP trail.

I'd look for lighter weight tires with minimal or no tread. They'll be a little more efficient on the trail. Knobby tires would be more useful for rough gravel roads, but these trails don't have a surface like that. You don't need the "puncture proof" commuter tires, either -- those are heavier and stiff, to avoid cuts from road debris.