Many times insurance companies will either require or give you a significant discount if you store your antique car in a garage. But garages are expensive. So why not store it in a large shed?
A properly built wood floor can easily will handle the weight. If you’re still concerned about the floor holding the weight you can place a second layer of plywood where the tires run.
This shed doesn’t need extra room to work around the car because you can transfer it to your garage when you need working room. The door can be a fancy overhead type or less expensive double doors.