Hi @Armillaria
Welcome to Food Talk Central. Let me give you too much information. 
Good questions and maybe other food talkers will chime in. I think folks like Arnett Farms and Ken’s Top Notch for citrus and apples in the fall.
The big farmers markets with every vendor are in Santa Monica (various locations) and Hollywood (Ivar). I prefer the smaller farmers markets - Bev Hills, Culver City and occasionally Larchmont in a pinch. Because I have a tendency to over-shop the big markets are overwhelming for me.
Here’s info on my spots:
- Beverly Hills FM (Sunday) is my fave. It’s a convenient drive from my ‘hood. And it has everything for one-stop shopping - excellent vegetable, fruit, meat, seafood, dairy and prepared food vendors with enough of what I call the designer vendors (tenerelli, harry’s berries, weiser, jyan isaac bread, lodge and more). With the fall season starting I’m still discovering who has the best apples and citrus.
- Culver City (Tuesday) comes in 2nd. They don’t have Tenerelli’s (maybe now?) & Harry’s Berries but they have Arnett Farms and quite a few chef favorites like Underwood (Manzke is a regular), Tamai, Murray Family Farms. A plus is CC has more vendors who sell herbs, peppers and produce for Asian cooking than BH & Larchmont (see ramones family farm). If CC wasn’t on Tuesday I’d frequent it more.
- I put Larchmont (weds & Sunday) at 3rd. It’s nice, organic and my favorite seafood vendor (Dry Dock) is there on Sundays. But it’s really small and has few of the popular vendors of other markets.
https://larchmontla.com/larchmont-village-farmers-market/
Here’s another Farmers Market thread with more info on individual vendors.
Happy Farmers Marketing!