Terminology gets increasingly mushy as the years go on... but my standard advice for this question is not to discount 'touring' bikes. Actually nowadays this is pretty much the same thing, as far as I can see, as recommending a CX etc. One way or another what I'm talking about is a slightly heavier/stronger frame - built for luggage - with drop handlebars - and the necessaries like mudguards.
My touring bike has rarely toured... but is still going strong from the 90's as my main steed. I've had it over the top of the Pentlands, I've carried big boxes of compost and rubble, I've towed and carried kids, I've ridden it regularly (although not recently) on the weekly Edinburgh Road Club rides, and I have even toured with it a couple of times fully loaded.
Good tires - usually pretty high pressure - strong frame - strong wheels - strong rack(s) - good mudguards. Take off the clutter (extra/both racks) and choose higher pressure tires (the tyre width much less important than the max pressure) when you want a faster ride.
On a slightly wider rim you can go both directions - really pretty narrow all the way through to something that'll cope not badly with rough surfaces.
Lastly - don't discount less fashionable gear/brake levers. Mine are bar end shifters on which the indexing failed long long ago (so now friction only). One brake lever pivot was repaired with a nut+bolt somewhere about '95 and hasn't failed yet... Nothing against modern kit - but for this bike reliability and ease of repair has been great over the long term.
Oh - and of course there's very little left of the original bike by now - most stuff's been replaced (including the frame because of a design fault early on). Come to think of it the brake and gear levers and Brooks saddle may be the only original bits.