I usually keep the boat moving at the slowest speed for about the first 30 seconds, because if you are on some fish you might get another strike, unless king/BM fishing, then I keep moving but the other rod and rigger comes out right away. For Coho and Pinks you can get another strike if you keep motoring for a bit. Once you get the other rod out you should stop the boat so you are not adding force to the fight by continuing to move. I think it is hilarious when I see people silver fishing at 4-5 knots, get a fish, and keep going at the same speed. No need to trun the boat into the fish, unless you have a big king you need to chase because you are getting spooled. Just stop, let the catcher get the fish close, If I turn the boat It's so the we aren't bringing the fish right in on the stern and Downrigging equipment.

Do you already have Downriggers?
If you have electrics, set the automatic stops so that the ball is just under the surface of the water when the retreival stops kick in. That way you can hit the retreive when you get a fish on and not worry about 3 or 4 feet of cable still being in the water to get hung up on.