How to play a selection

I select a small part of a track, now I want to hear it. When I hit space, Ardour plays the range (i.e., all tracks) but I want to hear this part of this track only (the selection). Preferrably without needing to play with the solo/mute buttons.

This is so basic that I must be overlooking something very trivial…

I believe what you are looking for is the audition tool:

http://manual.ardour.org/ardours-interface/the-toolbox/

Ben at Harrison has suggested a new workflow for auditioning in the future and I believe is implemented in the newer versions of Mixbus already:
https://community.ardour.org/node/15435
Not sure if the plan is to incorporate this in a future version of Ardour or not at this point, but worth keeping in mind.

         Seablade

Nope, the audition tool plays all tracks.