Get the widest tires you can fit in your frame and fork, and inflate them to half-way between the min and max of the tire range. Tires that deform when they hit an object are much less likely to puncture. (Think of how much easier it is to pop a fully-inflated ballon with a pin.) Wide tires enable you to run lower pressures without pinch-flatting. It is also far easier to get the tire and tube set up without pinching the tube (which also might be a source of weakness that eventually results in a leak).
I ride 38mm tires on my road bike, and weigh about 50 lbs less than you do.