I'm getting a new headset soon, but haven't decided what kind.

One factor that will affect my decision is the need for press adapters. I don't want to have to buy additional stuff. If I already have the Park HHP-2 press tool, will it work with any headset? Or are there some headsets I should avoid if I don't want to buy adapters?

This is for a regular 1 1/8" threadless headset.

Thanks!