I usually run four or six pound test mono; I try to match the color of the water but it likely does not matter. I've found that sea-run like to hide under obstructions and under cut banks. You'll also find them sitting in tail outs waiting for food to wash down into their face. Deep or shallow is mostly irrelevant in rivers, it's more about the reading the water and finding places they will lie.
Spoons and Spinners will work fine for sea-run, worms or single salmon eggs will work really well too. They tend to be hungry little buggers and less than particular in regards to their diet. Also, crawdad tails work really well. Pull the meat out, run the hook through it, then put the egg loop around the meat to secure it. Cast gently.
Try silver or brass colored Mepps spinners in size 0 or size 1 or half'n'half Dicknite spoons, those have been my go to hardware since I was a child. Silver or Gold/Brassy colored Hotshots in the second and third to smallest sizes will also produce result, especially around tidewater and in deeper pools. I've also taken to replacing the treble hooks on all the aforementioned lures with Gamakatsu single siwash hooks of matching sizes. They are sharp and they don't tear the fish up if you want to release them.
I don't have a ton of experience fishing for them in salt water, though the guys around the Puget Sound do pretty good with flies, spoons, and spinners. It is a catch and release fishery in the Sound.
I know that in your area there are a number of bodies of water that still allow the harvest of coastal cutthroat but be sure to check the regulations for the location you're fishing. Many coastal areas have been changed to catch and release only fisheries.
Stay legal, stay safe, and Good Luck!
