I am an expert fish smoker....I LOVE to smoke fish, mostly steelhead, but also salmon, as well as beef jerky and smoked pork. Mesquite might seem like a harsh wood for smoking fish, but it actually turns out superbly well. A lot of myths surround wood for smoking. Actual blind taste tests have proven that woods like douglas fir and western cedar are actually almost indistinguishable from classic smoking woods like cherry, apple, maple, alder. Mesquite wood is actually perfectly fine for smoking fish. I have smoked many salmon and steelhead with mesquite chips, and people love it.
Brine. Less can be pretty simple, yet delicious. One part sea salt to 20 parts water is good for average fish. Oilier fish, like spring run chinook or sumer run steelhead is better at about 1 part salt to 16 parts water. I go by parts because the quantity of fish can vary so, so much. One part each of granulated sea salt, one part white sugar, one part brown sugar, and then 20 parts of cold water makes a good basic brine. You can augment the brine with any of fifty substances. One part honey is a NICE addition to a brine. So is a small amount of garlic powder, allspice, sage, cumin, Worchestershire sauce, and on and on, ad nauseum.
If you have two, 25-pound chinook cut up "one part" is eight full ounces of salt. If you have five small trout, "one part" of salt can be 3/4 of an ounce.
Brine the fish 12 hours for thin fish like trout, 24 hours for thicker fish like salmon. If your smoker is HOT, brine larger pieces. If your smoker is cool, or cold, brine smaller pieces. After brining, rinse the fish, rack it, then sprinkle on granulated garlic and ground black pepper on each piece, and LET IT WARM UP TO AIR TEMPERATURE BEFORE introducing heat to it! THIS IS THE CRITICAL ASPECT!!!!!!! As the fish warms up, a clear glaze called the pellicle, will form on the outside of each piece of fish. Introduce heat slowly, with the lid open for an hour or so, then close the smoker. If white gooey liquid oozes out of the fish, you have lost the soluble proteins in the fish, and it will be dry and flavorless, and it will have happened because heat was introduced to cold fish too rapidly.
How long to smoke depends on the amount of fish in the smoker, ambient air temp, and the heat of the smoker's fire or heat source (electric/gas/coals,etc). How long to smoke also depends on the degree of hardness/moisture you want in the fish. There is hard-smoked and soft-smoked fish, as well as in-between.