Part and parcel of 'getting the boat moving' is resisting the impulse to put the helm over for the turn before steerage is attained... doing so simply puts the brakes on and increases side motion in many cases.
Keep the rudder centered until it will actually do something for you.
Also, once you know how much propwalk rotation you'll experience, simply point the boat at an angle such the the propwalk will straighten you out about the same time you start moving and having steerage.
All that said, though, there ARE some (actually many)designs that will not respond to any of these techniques. A short cord fin/spade rudder is always going to do OK in the right hands
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)