The newer Miatas have about 75 More HP at the wheels than the originals, hence it has the power to spin the larger 17" wheels. With the older models, they used a smaller wheel due to the low HP.
You will want to most likely go the 15" wheels. It will give you less unsprung weight than a heavy 16" wheel and give you more tire sizes than the 14" wheels.
A 16" or 17" wheel will add about 5lbs per corner affecting your handling in a bad way. Loss of acceleration will be noticeable as well, especially with 17's. A 14" wheel is a great choice, but you are going to be limited in High Performance tire sizes. This will also effect the cost of the tires as well. A 205/50-15 tire is sometimes more economical than the 185/60-14 which is a much taller and thinner tire.
If you want a good balance of lightweight, with a better choice of tire sizes and brands, I'd definitely stick with a 15".