Qt on BBB with Debian OS


I am planning to run Qt on BBB with Debian OS. I am looking for suggestions to choose the most lightweight & stable version of Debian environments. I need suggestions on the following topics considering my task is not too much heavy from Qt side

  1. Is it possible to run Qt on IoT(without destop) distribution of Debian?

  2. Is LXDE the best environment to run Qt as it is claimed to be most lightweight & stable version among all?

  3. Is there any other supported os that will perform better than debian, if I am just running Qt.

  4. Any other specific suggest for Qt versions