Q400
Flight Crew Air Transport Pilot (ATP)
Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Wake Vortex Encounter
Flight Crew Returned To Clearance
Procedure; Environment - Non Weather Related
I was pilot flying on climb out from SEA; we were encountering mild wake turbulence following the preceding aircraft.  SEA tower did not issue a turn to the east with the takeoff clearance.  On climb out of the SEATTLE4 departure we were eventually given a turn to 140 and a hand off to departure.  The First Officer (FO) checked in with departure and they told us to turn direct to a fix on the route.  They did not clear us higher than the initial 3000ft.  The FO commanded my FMS to proceed direct to the proper fix; I verified it and told him to press NAV.  All while this was happening we were encountering mild wake turbulence; a new turn; and level off at 3000ft.  I began the turn to the fix after verifying it in the FMS and commanding NAV.  I started the turn before the flight director caught up to the proper turn direction.  I overshot the level off at 3000ft.  The FO called 'altitude' when he noticed that I didn't level at 3000ft.  I leveled off at approximately 3120-40ft and returned to 3000ft.  Soon after we were cleared higher and proceeded uneventfully to destination.The cause of this event was my leading the turn and momentarily disregarding the HUD cue; while waiting for it to catch up.  In disregarding it and trying to hurry up into the turn I lost the valuable level off pitch guidance as well.  I was using the flight director but not following it.   With the distraction multiple changes it needed to be used completely or not.   The wake turbulence was a factor in that I wanted to turn out of it as soon as possible.
Q400 Captain reported an altitude overshoot on climbout from SEA; citing a wake turbulence encounter as contributing.