Figure on $90 dollars or so. Both http://www.primetimeshuttle.com and http://www.supershuttle.com have online quote capability. Note that the private van quote might include the gratuity, while the shared van doesn't, so factor that into your spreadsheet.
I am using Golden West Express (www.goldenwestexpress.com) for 6 people in December. $75 each way and they do a grocery stop for free. It will be nice because it will be late at night and I will have my parents with me and we don't have to do stops for other people at other hotels.
By FAR the cheapest way would be to rent a car at LAX that will hold 6 people (maybe a minivan or SUV). Check priceline. You should be able to get one for about $40 per day.
For a short trip, if you can indeed find a minivan for that cheap, $40 a day is good. However if your trip is longer than 4 days the route of shuttle or private limo company like Golden West Express is probably still the best bet. I