We use Colonial Airport Parking and have never had a problem. You can print a coupon from www.longtermparking.com. The cost with the coupon is $7.50 per day, which includes all taxes, and the 7th day is free.
We used to use Winner Valet...they will bring your car to baggage claim for you!! They do guarantee lowest rates too. But, last year (& this year too) we are just sleeping at the Reniassance Hotel there. You can buy a park and fly package...only costs us about $10-$15 MORE for the room vs. parking alone. We decided to start taking the first flight out in the mornings cuz when we would take an afternoon flight, it was always delayed. Now, we drive to airport the night before (at our leisure and not during traffic), sleep and get up early the next day and I'm at Disney by 11am!! Just something to think about if you want to go early, if not, we always used Winner. (They will also maintenance your car if you want--wash, oil change, etc.....)
I just book for park sleep fly package for $99. Last year we parked at airport, it was $8 day cost us $56. It was well worth the package especially since our flight leaves at 6:05am.