Your first group ride in LA
If you're coming from running you'll show up with a lot more engine than handling, which is a specific and fairly annoying way to be new. This is mostly about not being an agent of chaos while the two catch up.
Get ten or so rides in before you join a group - probably more than you think you need - then start with Rapha's Better Than Brunch on Sunday, which is a great first ride. Sit at the back for the first hour and mostly just hold your line rather than trying to be useful. Be open to advice from more experienced riders!
What gear do I need?
Before you join one
The ex-runner problem
Aerobic fitness transfers to the bike almost immediately and bike handling doesn't transfer at all, so you turn up with an engine that is months ahead of your balance and hands. Going up hills can be really entertaining - people will joke about no ebikes allowed and you can enjoy that.
Where it stops being funny is inside the group. Sprinting past someone in a group catches a lot of folks off guard and spooks them, and a spooked rider makes sudden movements, which is more of a problem than your speed is. And if you don't let the handling build up to match the engine gradually, those surges are exactly when you end up bumping into random things.
Pretend you're a cruise liner
Pretend you are literally a cruise ship. Enormous, full of inertia, incapable of doing anything quickly. Wind the pace up slowly, pass people gradually and in a straight line, and change direction like it costs you something. It sounds like a mood rather than a technique but it covers every specific rule at once, and the only exception is when something is coming at you the other way.
LA specifically
The rides here are long and they climb, so the honest thing to know is that a Saturday group ride is often five or six hours and somebody will suggest extra credit up Mandeville at the end of it. That's a real day out, not a spin, and it will find any hole in your fueling. You need to have gels or snacks ready and at least two bottles.
Concretely: start with Better Than Brunch on Sunday, it's an easier day and a great first ride. The Saturday social is good too if you're an ex-runner and reasonably fit, though get your weeks of balance and solo riding in first, and show up with clipless or you will get judged. Both are on the Rapha LA events page.