[DuckRyder]

Valving differs by model of car but it should shake out like this.

The TC or touring is a stock replacement type of shock with a conventional design. You should find it slightly stiffer than OEM.
(Remember when there are BOGE automatic and BOGE turbo gas; I actually like the turbo gas.)

Comfort should be a mono tube design, with the next step up in stiffness.

HD is a monotube with firm valving.

Sport is a monotube with firm valving for lowered cars.

You can't use sport with stock height springs, and for BMW applications the HD and Sport are either identically valved or very very close, the distinction being whether the car is on short springs or not.

I find that Bilstien mono tube shocks can be harsh over sharp bumps. From your description sounds like The TC or Comfort would be what you are after.

If money is not an object, you might look into KONI (yellow) sport with external adjustment.