We also need 8 seats, and usually have some "extra" people with us, so we've rented LARGE (15 pass) vans 3 times now. Once from
Budget for about $500/week (about $150 below the regular price, but I booked 8 months in advance) which was fine, and twice from Orlando Car Rental. I would highly recommend Orlando Car Rental. Their prices are competitive, and the owner, Richard, is great to work with. Their website is
http://www.orlandocarrental.com/
We were concerned about space for all our luggage, and Richard actually removed one seat out of a large van so we'd have more room in the back. The office is in a hotel close to the airport, and Richard will pick you up at the baggage claim area (usually in the van you'll be renting), take you to the office for paperwork, and then you're on your way to WDW! I thought renting from a company actually located at the airport would be more time-efficient, but it wasn't. It took just as much time at the Budget counter as it did going to the Orlando Car Rental office.
On one occasion, something went wrong with the van (minor, and I don't remember what it was, but we couldn't drive it) and we had to take a cab to our destination that evening. Richard reimbursed us for the cab and had the van all fixed up the very next day. He's a pleasure to rent from, and I'll probably do so again next time we go.
We also homeschool, and just returned from a week's trip. Hope your vacation is magical!!