3) Promotion of best practice / skills development
For me, the most important of the three is the selection of projects. The reason for this, as regular readers will already know, is that perfect execution means nothing if you’re executing the wrong projects.
I sometimes see PMOs who focus exclusively on points 2 and 3. They imagine that the “executives” magically pick projects that are the right projects and that the PMOs responsibility is simply to make sure they are well executed. This often leads the PMO to rush out and implement project portfolio management (PPM) software to support project execution and governance.
Of course, I'm not suggesting that project governance and adopting best practice are not important. They are. I'm simply suggesting that there is a natural order to these thing: get good at prioritization first, then you can worry about executing the projects better.
I dare say many people out there will disagree with me. That is your right, but please, please, don't ignore the project prioritization process.