Planting a cover crop is preferable to leaving the ground bare, if you will not plant a market crop this Spring.
I suggest a soil test so you know soil pH and any soil nutrient needs
before considering which cover crop to plant. California ag agents have the reputation of being very helpful.
While growing, cover crops outgrow weeds, smothering the weeds.
When turned under, cover crops add nutrients and improve soil tilth.
I use mixed Oats and Winter Wheat, which mature successively, for a fall/winter cover crop, Sunn Hemp in the Summer. May experiment with Buckwheat and Clover.
Legumes add nitrogen. (clover, beans, peas)
Cover crops are usually in the ground four to six months, then disced under.
What works well in Florida probably will not be optimum in California. California/western grown seed will probably be most successful for you.
A number of game food plot seed mixes make excellent cover crops and may be cheaper than individual seed types.
Many cover crops are $25 - $30 per 50 pound bag in Florida.
LINK:
https://hancockseed.com/collections/cover-crop