Don't buy a brand new board for your first one, find a local surf shop (there are MANY in San Diego) and tell them you're a beginner and they'll probably hook you up with a long board. Get a used one, make sure it doesn't have any holes in it, you can get one for under $400. If I were you I'd make sure the board was at least 8 feet.
Reason why people always learn on a longboard is because paddling is a lot easier, its easier to catch waves, and its easier to balance because there's more surface area. Don't even attempt surfing anything below 7 ft as a beginner! You will be really frustrated.
I know shortboards "look cooler" but they are extremely hard for a beginner to paddle and balance on. In California in the winter you need a wetsuit. You get really cold in the water after about 30 minutes, even in the summer most people use wetsuits.
You can get a cheap one for 100-200 just go into a surfshop and try some on. (Make sure it's not too loose else water will seep in!) Of course the really good ones cost at least 300. If you can afford it, it's worth it in my opinion.
As for beaches - any place you can find that has breaking waves and uncrowded is good for a beginner! There are several beaches in San Diego (I'm guessing - not from so cal) where you have small rolling waves. Maybe San Onofre would be good.
Be creative and find beaches yourself - that's part of the fun of surfing, or of course you could just ask a local at a surf shop. Advice - Go early in the morning or during "work hours" to get the best waves. Be nice to people out in the water.
If you see an experienced surfer, make sure to get out of his/her way when they are paddling for or riding a wave. Never catch a wave someone else is riding! The surfer closest to the "peak" (the tallest part of the wave) always gets the right-of-way, and catching a wave he/she has caught already is called "dropping in" and you could potentially get yelled at.
Also, over the course of learning how to surf you probably will get yelled at. Happened to me like five times. Just apologize and don't take it personally.
And when you're learning to surf, don't get frustrated. Try riding on your belly (like a boogie board) in the white-water first, then try standing up. Once you can ride the white water well enough and balance then go for the real (unbroken) waves and remember to catch it at the peak.
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