Probably the first one with drop bars. Although pick just about any hardtail mountain bike from 1981 to current, slap a rigid fork on it, and some drop bars. Go wild! Alternatively there is any number of cyclocross bikes that would fit the bill. Alternately to that, pick any touring bike. Same result.

And if anyone is worried about braking, remember that we old mountain bikers did just about everything that is ridden today on rigid bikes with cantilever brakes. Somehow we lived to become old mountain bikers.