I'm out on Cali, fish 100% from shore, and use a dropshot 90% of the time. A big part of that is because it's a technique I picked up early when starting to fish freshwater, and had a lot of success with it, so I never bothered to learn other techniques when I knew I'd get bit on a dropshot.
I always use a size 4 or 6 hook, a 1/4 or 3/8 bakudan weight, and small plastics (3.5-5") nose hooked for better movement in the water. Whatever plastic you use be sure to drop it right in front of you and see how the bait reacts in the water based on how you impart action. When nose hooked you really don't need more than a light tap of a fingertip or tiny flick of the wrist to get the plastic to move. It's really easy to work it aggressively like say a c-rig or t-rig bait but that'll give the plastic unnatural movement.
You really want to keep the bait out in the depth zones you want to check for as long as possible - after casting I'll spend 2-3 minutes at that depth lightly tapping the rod every so often, reel in a bit, fish that depth, reel in a bit, fish that depth, repeat, until I find where the fish are. Little fish will aggressively hit the bait, the larger fish will be very subtle where you may not even feel a tick, but a light pull on your line that will get heavier.
The hardest part is being patient with working the plastic. I've started to fish more reaction type baits like swimbaits/squarebills/vibrating jigs and noticed that once I fish those, and go back to the dropshot, it's really difficult to be patient.