Hi Typhoon Guy,
I'll mostly just back up what others have said:
1. A shuttle from LAX to Anaheim is usually a safe bet, especially if your party is fairly small. I tend to avoid the Airporter Bus; I've had some uncomfortable rides and it can take a long time.
2. 4 days should be OK if you are avoiding Thanksgiving, but you might want to consider 5. You'll need to schedule some weekend days to be sure that the parades and shows are available (some are only shown weekends during slow periods). You might also keep in mind that most holiday decorations go up early in November, so mid November is a lovely time to go. Keep in mind that Veteran's Day can be a bit crowded though.
3. Which hotel depends a bit on your wallet, your party, and what deals might be available. You should be able to work a 4th night free at the Disney hotels. Like others, I like the GC for it's style and location. The DLH is less expensive, has bigger rooms, but is further from the parks. It's pretty festive, and is a good bet with kids. You should be able to get in some pool time in Oct. and even November, and as pointed out, the Neverland Pool is fun. PP is nice, but farther still. It doesn't feel much like being on-sight to me unless you have a park view room.
4. I could not imagine going to WDW without staying onsight. The benefits are significant, the resorts are so much closer, and some of the resorts are so lovely. The benefits of staying onsight at DL are limited. You do not have the EE benefit, and can still be within walking distance staying off-site. Aside from the places directly across the street, there are several very nice hotels and suite hotels with shuttles every 1/2 hour (although the ART system gets mixed reviews). Nevertheless, like some of the others, I still find that I stay onsite most of the time. It's very nice being submerged in the magic, the Disney pools are more fun than off-site hotels, and I think the Disney properties are significantly nicer than anything else within walking distance (<1/2 mile or so; you don't want to have to walk back to the Hilton after walking the park all day). Since you should be able to pick up a 4th night free deal with off-peak season rates, on-site may be worth it.
5. Like Buckimion, I usually price things on Expedia or other travel website, but then tend to book things separately. I've tended to get the best airfare deals using the airline web-sites. Shop around. You shouldn't need to prepay for ground transportation if you choose a shuttle, airporter bus, or taxi.