5 x 120 bolt pattern, 38mm offset. Your offset can differ by a few mm, but ultimately you need to make sure that the brake calipers don't hit the rim. 17 's or 18's will work, your tires should obviously be low profile.
Changing wheel/tire size affects a lot of things: suspension handling, speedometer, and braking. In general, a lower profile tire will stiffen up your suspension, but a harsher ride as far as bumps go. And the heavier/bigger the wheels, the more braking power is needed to stop the car. Speedometer accuracy is a function of the wheel diameter. To calculate this, go to: http://www.miata.net/garage/tirecalc.html