Most tourists use a light tread to cope with occasional tracks and trails yet maintain road efficiency. I use Schwalbe Marathon, a standard but good quality commuting tyre and have ridden miles of tracks, trails, mountain paths and even beaches.
Tyres are one of your most critical components. They affect speed, comfort and braking and are the main cause of stoppages. Dont go for the low end budget option, spend a little more and you will not regret it.
High end touring tyres are quite expensive but the standard Marathon (or other commuter style tyres) is perfectly good.