Both Shane and Paul covered it pretty well.
In this stretch of the coast, in the surf - a type VI or VII fast sink head will be your weapon of choice 95% of the time, so I would start with that - whether you are talking about a shooting head or a integrated line. And given the time of the year, I would just get your 6 wt set up and start fishing as soon as possible - you can put off decisions about the heavier rod for a while.
I started off fishing with a 9 wt rod years ago, and I am slowly over time finding out the things that lighter rods are capable of, so I most fish now with a fast 6 weight (Scott X2S) + 240 gr type VII head, and intermediate sink running line. (A few weeks back I C&R'ed a 25# leopard shark, tail hooked, in about 12 minutes with the 6 wt).
Note that if the surf is higher, such as in the winter months, I will switch to an 8 wt (and older Scott STS) and about 300-320 grains. You simply need more weight to control your drift as the surf gets heavier.
There is one specific situation that I am aware of where a Type III could come in handy: fishing for mid-column species such as YFC over rocks, with a sinking fly. But even in this case, you can get by with a Type VII and a quick pace to the retrieve.
There are some sharpies in LA county that use intermediate heads when making distance casts for corbina - this allows for extremely delicate presentations to fish in thin water. However, part of that fishing style depends on the behavior of fish that only a few beaches in LA county are able to elicit from the fish. (I have seen corbina behaviors in LA county that I have never seen even once in VC or SB County, and that has very much to do with both water temperature and beach slope.) So, the fishing style up here is a little bit more "up close at the edge of the beach" in slightly sloppier water with more current, so even though a fast-sink head is less stealthy, it has presentation control advantages in heavier current over an intermediate-tip head.
As far as uplining goes, one of the differences about casting a fast-sink head is that - due to its thin diameter and reduced drag - you can develop much faster line speeds than with an equivalent-weight floating line, and this corresponds to more rod loading on the back cast for the same line weight in a floating line. (And having said that, I see that using 240 gr. on a 6 wt rod is "uplining by 3"; hey, what can I say - that Scott is a mighty fast rod).
Since you are planning on doing the shooting head thing anyway, you might consider buying a standalone running line (SA or Airflo) and 34' of T-8 for the 6 weight - and chop the head back one foot at a time to see what grain weight you like. All things considered, T-8 is inexpensive. It doesn't cast as well as a tapered head, but it will give you a good idea what kind of grain weight you prefer.
Backing? If you thought you would only use that spool for the surf, then for sure I would say "Just use 30# Dacron which is spliceable, such as Cortland's Micron". If you were going to have the reel/spool do double duty, say fishing from a boat in kelp beds, it can be nice to have GSP's kelp-cutting capability.
hope that helps