High key pictures have varying levels of contrast, so it depends. There is absolutely no reason why you cannot get high key pictures with any film and developer combination out there. You just have to know what you want, and be willing to do enough informed experimentation to get it.
I would say that a good starting point with Tri-X (320 or 400), or any film, is a run-of-the-mill developer like Ilford ID-11 or Ifotec HC (equivalent to Kodak's D-76 or HC-110). Learn to manipulate exposure and development with a simple combination like this, and you will be able to learn the basics of getting what you want, and apply it to anything else down the road.
In general, for high key pictures, I will shoot a flat film (like Tri-X 320), overexpose one stop or more, overdevelop +1 or more, and print on a hard printing paper/high MG filter using a soft paper developer. Some of my favorite films for high key pix are Efke 100, Tri-X 320, and Delta 3200.