Well, since we are trying to "be careful" here, let's also make sure we be extra careful in saying that the atomic orbitals somehow implies a "velocity" or speed of anything. It doesn't. By saying such things, we are already implicitly implying a well-defined charged particle moving around. You don't have such things until a position measurement is done. Before then, an electron in an s-orbital, for example, has no well-defined position and identity. Rather, based on the wavefunction alone, it is "spread out" in a uniform sphere around the nucleus. So the electron is everywhere simultaneously (which is connected to the Schrodinger Cat-type puzzlement - another illustration that things in QM are interconnected). This is how we get an angular momentum of zero for the s-orbital - from the geometry of the orbital itself.
This is another illustration where our social language can cause many confusion in trying to describe things that have no linguistic equivalent. As soon as we say "electron moves in an orbit", a whole range of implications kick in. We automatically imply that there is this well-defined object that we can track along the way and moving in a well-defined trajectory. QM implies no such thing, at least as far as atomic orbitals are concerned. We have seen a whole zoo of evidence where an "electron" can simultaneously spread itself into many locations to produce unclassical effects (bonding-antibonding bands, etc.) Zz.