My advice is to check everyday; rates fluctuate so much even as your trip gets closer.
IMHO, stick with onsite rentals like:
Avis, National,
Alamo,
Budget, Dollar, and L&M...this is MHO only as I do not want to get my luggage and then lug it onto a shuttle and then lug it off (my kids/car seats too!) and then get my car. I'd rather get my luggage and walk to my rental car and then I'm off; IMHO, of course.
I prefer National but would go with Alamo (their sister company) or Dollar if the price was right.
I'm paying $111 TOTAL (Disney Club discount and coupon) for a week Full size (Nov/Dec). At first it was over $200 and then it came down several times before I got that great rate.
Some companies, if you join their club (National = Emerald Club) you can even skip the counter. I belong to this club and it's heavenly! I go pick my own car and I'm off! No counter or shuttle.
Right now, it is $147 total for a Full size at National but that's with the Disney Club discounts. It's $166 total with the Entertainment book. Discounts available are Disney Club, Entertainment book, a wholesale club store like BJ's even
Walmart and Vacation Outlet's website have discounts you can use!
Regarding a Full size being big enough for 3 adults and 2 kids with car seats and their luggage, it will certainly be tight but possibly doable. We are a family of 4 with 2 car seats and at least 4 suitcases and the worst part is getting to the hotel and to the airport with the luggage. Once you get that out, the car is more comfortable. It will be tight though. You may want to check with Dollar for a mini-van as they usually have the best minivan prices.
Good luck!