I am afraid I don't know which folder you have, but in general one would want to choose tyres based on what features one wants most (e.g. speed, comfort, lightness, puncture protection etc.), and as in most things there will be tradeoffs and no tyre has all the best features.
Unfortunately one of the negative effects of small (20" e.g.) wheels is that potholes can feel like underpasses. Assuming your folder has no front/rear suspension, for shock absorption the tyre design characteristics that matter most are the volume of the tyre, the side wall flexibility and pressure. For that specific purpose while offering reasonably low rolling resistance for road use, one of the best is Schwalbe's
Big Apple. Obviously the wider the model the better pneumatic shock absorption it can provide, but you do have to check that your fork and rear triangle have the clearance (vertical as well as horizontal) to accommodate the tyres you want.
A disadvantage of the Big Apples, however, is that they are not light. If you want high road speed and a good degree of puncture resistance, then a narrow slick such as Conti's
Sport Contact 20x1 1/8" (assuming your rims are not too narrow for them, see bottom of
this page) pumped up to the maximum design pressure will be great - but the ride can be a bone jarring experience.
Hope it helps.
