My mum lines in North California (and I have family in the South), so I've done that trip plenty of times. Everytime i visit i try do a west coast trip. Done it in campervan over three weeks once, and the other times with a hire car staying in motels/hostels.
WHERE TO GO
LA to San Diego is only two hours so its easy to buzz back and forward. Trestles is a must - crowded, but have uppers, middles and cottons as well as lowers, so plenty of waves to go around. Cardiff/Encinnitas and that area is a good place to base yourself - good waves and an hour either way for lots more options (Huntington, San Clemente to the North & Sa Diego Breaks to ther South). When we were there we stayed around there, surfing there when there was a wave and heading to Blacks which gets a load more swell when it got small.
Lots of options in Ventura, beaches, points and reefs, worth a visit - and places to camp i think.
If you decide to head North of Ventura, the options for waves thin out a bit (you drive a long time between breaks, whereas in the south, its just break after break), though the Big Sur drive is mindblowing, especially if sunny, and there are breaks around there, rarely see a crowd, in fact ive never seen anyone surfing there. Some good waves, but some very average ones (Pismo, crap wave, fun place!).
On the campervan living, the one think i noticed is that wild camping is not that easy! EVERYWHERE - laybys, car parks etc etc have a sign up saying 'no overnight parking/camping'. This is the whole way up the coast from San Diego to San Francisco. It is particularly hard in the south where the place is very urbanized. However, we did get away with it - WALMART parking lot, out of the way laybys etc, but be warned everywhere has a sign! Occasionally stayed in campsites, think it was about $30pn (this was out of season, we were told you may need to make bookings in peak season). Don't think there are any campsites in Huntington to San Clemente area, though there were plenty between there and San Diego, they are all state parks so are easy to look up. The one at Encinnitas/Cardiff is particularly good, fronts the beach, great waves there.
Board shopping in CA is a lot of fun, there are SO many good boards and lots cheaper than the UK. I have the same problems with boards and airlines, so have bought cheap secondhand ones there. I got a two decent condition lost... boards for 120bucks and 100. You will have no problem picking up second hand boards - lots of places in every surf town> Not sure about selling, I sold a board in a shop, but they didnt want to give me cash upfront, they sent it on when the board sold (to my Mum - so was quite straight forward), but to be honest you can get boards quite cheap and I imaginer you will be able to sort something!
You are going to have an awesome trip, CA is a blast!
I'm quite likley going to there myself actually!!