You can lock into an axis or inference direction with the shift key. The axes directions can also be locked in with the arrow keys as well. I'm not sure how the gizmo is more helpful. I use ThomThoms vertex tools gizmo and it's OK for some things but it means you can't get the snaps (as far as I can tell). If you just try moving a little before you get a constrained direction it will tend to just snap where you don't want.Sometimes you have to move too far or the opposite direction first to find the axis direction. But no there isn't a native gizmo for SketchUp. Try some of the tutorials on the move tool.