I really wouldn't change the wheels. To start with, you might find it difficult to even find a 16" wheel that would fit, but even if you could, it would ruin the looks of the car and kill resale value.
I think I'd go with replacing the current tires with non-runflats. You'll find this makes a tremendous difference in the ride, handling and quietness all by itself.
For a spare, you have two options, get a spare tire kit or get a plug kit, a small air compressor and a AAA card. You'll probably find that the latter will take care of all your needs.