Opinions vary widely. It's good to try everything and decide for yourself.
I like 65# Power Pro spectre braid. I get the common dark green color that feels hard and slightly bumpy to the touch. It casts very easy for me and I never have problems. 65# can cut through kelp tangles easily.
I have tried another slippery feeling braid ... "super-slick"? something like that. Didn't like it at all. Had some birds nests and replaced it with the standard durable Power Pro that I am familiar with.
For my bait leader I like 40# Blackwater fluorocarbon shock leader. It's a little more expensive, but it's a luxury to use. It is tough and stays straight without memory curl. I think it's more abrasion resistant than other common brands. Since I'm only making leaders, I don't mind the price. For SD Bay I have a spool of 25# Blackwater. Squidco has a full supply of all sizes of Blackwater products.
For my sinkers on a 3-way rig, I probably have a lifetime supply of old 25# and 15# Big Game Trilene mono that I'm using up. I usually use the 25# because I can still pull pretty hard to free my weight, but it's also relatively easy to break off when necessary. My weight line is scrap, so anything will do. It gets scuffed up so I change out my weight lines regularly.
Opinions vary, but I generally like the convenience of circle hooks. 8oz torpedo sinkers are the size I use most for the ocean. For jigging I am currently using megabaits for a fast descent to the bottom and I'm exploring slower Shimano flat-fall lures for reeling up and fluttering back near the bottom. For top-water casting, I still like my old Tady 45 lightweight irons. If you are interested in rock fish, etc., dropper loops always work and squid are easy to carry as backup to making bait. For making bait I use cheap sabiki's from Squidco that are about $1.50 each. Get the sabiki's with a 30# main line because you might pick up something bigger than bait. For the weight on my sabiki I use a small salas iron, which can also be a multi-purpose attraction when I drag it behind my kayak heading out to my fishing destinations.
For my weight lines, I like to use a surgeons loop so I can easily slip weights on and off. My other knots for connecting lures, hooks and swivels is usually a palomar knot or a san diego slip knot. For connecting my Blackwater leader directly to braid I like using a royal polaris knot because it's small and tight, and it slides through my eye guides easily. For my trap hooks I use a piece of 30# braid from the trap hook to the main hook. It's easy to have a snack bag of these pre-tied. Then I simply tie my main hook to my main line as usual.
Your 20# spinning outfit is OK for catching bait, but I think it would be too light for catching the bigger fish you want.
There are endless fun things to try. For La Jolla kelp beds, this is a good starting package that doesn't take much space. It gives you variety for different approaches to fishing and targeting of different kinds of fish.
Bundle and secure everything down flat or inside the hull before you go through the waves. It's good policy to be ready to roll and hopefully it won't happen. I think it's safe to say that everyone has lost gear that's not tied down. I certainly have, including my favorite deceased fishing hat that was tied to my head with a chin strap. It was one of those "oh shit" moments when my kayak decided to be a surfboard with a fun start but an unhappy ending
