What kind of trails are you riding on? Either way, a new wheelset wouldn't be necessary.

If its just simple gravel trails, the 700x32 slicks would be fine.

If you're gonna do more MTB trails, look at some of the cyclocross tires, or 29er tires. Should be able to find a good set of tires to fit those 700c wheels of yours.

Largest issue is clearance - you need to make sure your bike has clearance for larger tires.

What bike do you have, btw? That would help us out easier in helping you pick tires.