MR2 MKIII wheels fit a MKI, and look very good. MKIII wheels are same bolt pattern, and are a direct fit. You will have to unscrew the "idiot mounting pin" from the rear wheels. The pins prevent the rears being installed on the front in a Spyder, since the rears are wider. Use vise grips or pliers to unscrew the pins.
Images by Skaughtto (with stock suspension)
The standard MKIII rear tire size has a larger radius than the MkI, so your speedo will read low if you use the 205 MKII tire size (speedo reading = 70mph, actual speed = 71.02). Using 195x50 will correct this (speedo reading = 70mph, actual speed = 69.8mph).
The MKIII tire size is 185 on the front, but for the MKI, a 195/50/15 works better on the front. There is also a wider range of choices in the 195 size.
The MKI lug nuts are longer that the MKIII and tend to stick out. The MKIII lug nuts fit better on the MKI with MKIII wheels. Excellent information at Kallist Motor Sports.
Mazda Miata wheels also fit -- verify which Mazda year.