For me, the best time to fish streamers - absolute best time - is when the water level is changing, i.e. rising or falling. This is especially true of migratory fish, which seem to wait for water level changes to move upriver.
For example, Landlocked salmon on the fall spawning run congregate at lake inlets, and while some will start up whenever they feel like it, most tend to move up river when water levels rise and the temperature drops. Also, a sudden drop in water level, especially at night or on a dark day can push the fish to move that are already in the river - at least the ones that aren't already at their destination. They move fast and can cover several miles a day.
Although I haven't fished for sea run brown trout before, from what I've read most catches of sea runs occur when the water level starts to fall following a heavy rain.
Shad do the same thing, they wait for the water to rise before they move. I would expect Sunday & Monday to be good shad days.
For trout in your local stream, I believe rising water (from my experience) is more productive for prodding fish into putting on the feed bag.
I usually base my streamer pattern based on water clarity. The murkier it gets, the brighter, or darker the pattern. The point is to increase the contrast so the fish can see you streamer.
I prefer bright yellow, or black. That was the idea I had behind one of the streamer patterns I came up with, which places a yellow saddle hackle on top of a black one in the wing, with the golden pheasant neck for the shoulder which is orange and has those black bands.
If the water is still relatively clear I usually opt for a streamer that approximates natural forage, such as a gray ghost, or similar.
If you do go out in heavy rain, be careful because even here in NJ water levels can come up fast, and you may find that you've waded somewhere you can't get back from very easily. Know the water you are fishing, and pay attention to how to get the heck out of the water fast if you have to. Safety first!