What should be the escape velocity for our galaxy and can we calculate it?
For instance, if we assume that we don't know the mass of our galaxy, you may consider it as small 'm'.
This is actually pretty difficult to do, because it depends on where from due to uneven distribution of matter (local parameters), how far from the galactic center due to radial velocity, the direction in which you want to reach escape velocity (how much of the radial velocity can be used), and that it's hard to estimate mass of the Milky Way (global parameters) and there will always be significant uncertainty with methods that are currently available to us.
We can probably expect a much more reliable overview of mass distribution, stellar velocities and total mass estimates once the Gaia observatory completes its billion stars stellar kinematics survey, but so far the best we have is probably the results of the Radial Velocity Experiment (RAVE) survey;
RAVE took a sample of 90 high-velocity Milky Way stars (some moving at over 300 km/s) for which their position and velocity was determined sufficiently precise, and then compared their movement to models of other, similar spiral galaxies, to reach an estimate of Milky Way's total mass at about 1.6 trillion solar masses. Once they had that, they could calculate estimated escape velocities for our stellar neighbourhood, for which mass distribution and radial velocity with respect to the galactic barycenter are of course most well understood.
Solar system's orbital velocity is estimated at roughly 220 km/s, and galactic escape velocity for our vicinity at about 537 km/s. So in the direction of Solar system's velocity vector, velocity required to escape Milky Way is ~ 317 km/s. And much more, if this Solar system's own orbital momentum cannot be used to full extent and a launch in other directions is required. This is of course assuming you can launch on a trajectory that avoids getting too close to gravitational influence of other solar systems.
Exact methods used to calculate this are a fair bit too complex to even attempt describing them here, so I'll refer you to some interesting sources:
And a bit lighter reading: