It depends on what type of towncar is being brought by the comapany. If it's a late model Lincoln Towncar, they have very deep trunks, could probably squeeze your luggage in there. It might be a tight fit, depending on how large the bags are, but it can be done.
Some companies have Cadillacs, which I think are nicer, but, they have half the luggage space. I remember I was with a fellow DIS'er, and they were going from Pop Century to another resort (off-property), and they couldn't fit all thier luggage into the Cadillac. Nice sedan, just wish they'd add more luggage space.
Not sure how pricing goes, but I know
FL Tours I know has a really nice luxury conversion van that would also work out well, and has PLENTY of luggage space. A regular van would also be fine... not as luxurious, but less cramped than 3 in a back seat of a towncar.