Going uphill air resistance isn't a factor due to lower speeds which means rolling resistance from your tires is the most significant factor besides bike weight that will determine your speed for a given power input. Any tire promoted as flat proof or highly flat resistant will be slow as will cheap Nashbar tires. The fastest practical 700c tire I've used is the 700c x 30mm Grad Bois Cypres.

You have to decide if you'd rather spend 10mins occasionally fixing a flat or spend hours riding considerably more slowly without any flats???