My definition of the word 'play' in this context means free movement of one thing relative to another.
If we agree on that definition, the play in all bushings/ball joints etc needs to be zero. Any play will result in uncontrolled suspension movement, a lot of annoying noise, and highly accelerated wear.
What you need to be concerned with is compliance. Bushings act like springs (and often, dampers too) which add to the true wheel rate of whatever they are attaching to the chassis. The stiffer they are out of plane, the higher general harshness you will have, but the closer actual suspension movement will map to the expected result from a given spring/damper/geometry. And vice versa. The stiffer they are in plane, the more they will affect wheel rate. The best solution from first principles and disregarding NVH is a bushing that has very high out of plane stiffness, and almost zero in-plane stiffness; spherical bearings get relatively close.
As you add in out of plane compliance (ie, reduce stiffness) you get better NVH - ie better 'ride' and less harshness over bumps/impacts.
Ciba's comment regarding tire stiffness is valid, and will be a major factor in the end result. If it's truly a track-only build that's going to run slicks or high performance/low profile DOT tires, you will want to keep that in mind.
If you actually are modifying an existing chassis, your best result is going to come from buying off the shelf parts. Particularly for Miatas, there dozens of options in the range between street replacements and full bore hard core track parts. Trying to engineer and fabricate your own bushings is non-trivial engineering; the money and time you'd spend doing it yourself will be better spent elsewhere.