Are you using a Floyd Rose? If you are, you'd probably need to adjust the springs at the back. I just changed my string gauge not long ago, and with some help, did up the springs and all to perfection.
You'd need to adjust the truss rod if your neck is not straight. You should change the strings first and then check if the neck is straight.
But actually, I prefer to have a bit of relief on the neck.
And the saddle too, thicker strings'd probably afford lower action, so if it buzzes(and it bothers you), then up the saddle. :wink: