After fixing up my father's old road bike, I no longer use my hardtail GT MTB that much. It used to be my only bike, and I used to almost only ride it for commuting and for getting around in general. With my new old bike, I realise I might as well use the GT for actual offroad cycling. I've ridden it a few times on local trails and such, and I'm pretty certain I need new tyres. The old front blew out, and the back has lost all threads on the middle inch or so of the tyre. (I've replaced the front now, with a very cheap temporary tyre.)

Can you recommend any specific tyres? Would I be better off with two different, or two identical tyres?

The bike has normal 26 inch rims. I'll be riding on all sorts of terrain. Trails, fine and coarse gravel, some mud, wet and dry conditions, rocky climbs, and so on.