A convertible holds almost no luggage. No matter which one you get. We have to take the top down to get a suitcase into the backseat because the trunk, if you're lucky, will hold only one - and that's if you get the Crysler convertible. Forget about putting anything into a Mustang trunk.
To make your moves easiest it may be best to rent either a luxury car with a big trunk or an SUV. Because you're moving around a bit, the extra cost involved for the larger cars would offset the shuttle/cab costs.