Welcome to Deeper Blue. There are very few SoCal divers here, so I'm probably one of the only ones who even knows the spots you ask about and I haven't been to them in a long time, but I'll take a stab at it.
Its probably been over 15 years since I dove Crystal Cove, but I think it is a good place for a beginner to start. However, it gets worked pretty hard since all of Laguna Beach to the south was closed to spearfishing a few years ago. There are spots to enter over sand beach rather than rocks. I think you may be right that sheephead are probably your best bet, although there is always a chance for a legal calico bass. There are a lot of areas of sand where you might find a nice halibut if you know what to look for. In fact the last time I dove there I recall diving between a couple of rock reefs and sitting the muzzle of my gun on the sand, only to have a halibut bolt out from under my tip. There is a chance for white sea bass too. In fact that was my excuse- I was looking out for a sea bass rather than down at the sand.
PV offers many more opportunities. Its one of the best spots in SoCal for white sea bass and many big ones have been taken there this year. But before you shoot one, make sure you are properly equipped with a decent gun and a reel or breakaway float line. As you probably know, you have to hike down steep trails to get to the water at PV, and then you have to hike back up with your fish. Some trails are worse than others, but none are easy.
At most PV spots you have to enter over rocks and it can be hairy if there is any surf.
I'm not sure what you mean by toothy, but I'm assuming you mean sharks. Last year I heard that there were an unusual number of 7 gill sharks there, but they don't attack divers. However, they can attack your white sea bass if its wrapped up in the kelp on the bottom.
Many divers are very protective of PV. After all, its right next to the Los Angeles Metropolitan area and when the word of white sea bass gets out, it can get very crowded. A friend of mine dove there yesterday and said the visibility was horrible and he didn't see any fish. But since white sea bass had been taken there the previous day, there were 10 divers on the spot. You aren't going to get a warm welcome, but they don't have any more right to dive there than you do. Just try to use common sense and don't crowd other divers. Watch how other divers enter and exit and learn from them.
I tend to focus on white sea bass, but of course there are also calicos, sheephead and halibut. And sometimes there are even yellowtail. I know a guy who took a 40 pounder diving from the beach last year.
You won't see me at PV. I'm too damn old climb the cliff, and not willing to tow my boat up through LA traffic to launch. I dive out of Dana Point Harbor. But if I can help with questions about equipment or anything, feel free to ask.