After reading the postings, I think a taxi is the way to go.
Anybody got an estimate how much it should cost?

Just to pile on, the walking times don't take into account how you can be stalled by traffic, not to mention other tourists and even normal, everyday people. You can't just go zooming along the sometimes narrow streets at top speed, crushing everyone and everything in your path.

I'd probably take the metro. It's a pretty sure thing, and it is fast. You'd get off at Ottaviano. I'd aim to be at Ottaviano at 8:15, to allow plenty of time for walking to St. Peter's, orientation, security, etc.

I'd take the Metro. It costs 2 Euro for two people; it's fast; it doesn't get stuck in traffic.

A taxi would cost about 10-12 Euro. It's impossible to give a real cost, since it's calculated by both distance and time (including time stopped in traffic).