Why did you have your car serviced in the first place? What "diagnostics" were performed? As Tony said, if your fluid levels were fine, your hose did not leak, and you have some other problem. Try to describe the symptoms in excruciating detail.

As to what to hose down: your driveway. You spilled antifreeze, which is poisonous to any animal stupid enough to drink it. Wash it away with lots of water,or soak it up. Make sure your alternator is dry before starting the car.

The radiator hose is a no-brainer; it is almost impossible to do it wrong, so don't worry about that. You want it tight enough not to leak, but don't go crazy.