We're big fans of LED lighting. It responds quickly, it generates almost no heat, it lasts for a long time and it uses minimal power. What's not to love?
We use LEDs from Diode Dynamics because they're the best ones we've found. They're made in the US to high standards, not just the minimum price. They've got constant-current circuitry to protect the bulbs from transients and offer a three year warranty. Even their lumen ratings are based on actual measurements instead of advertising promises. You can buy cheaper LEDs, but you can't buy better ones.
For the side markers, we have the option of amber and red bulbs that use your existing housings, or complete replacement housings that are either white or smoked when off but still light up the right color. Note that the complete housing sets are not made by Diode Dynamics and are sold in packs of four while the bulbs are sold in pairs.
If you have cruise control and you replace all of your brake lights (not tail lights), you'll need to add a resistor to keep the cruise control functioning. If you leave a single incandescent bulb, the cruise control will continue to function with no issues.
About hyperflash: the flasher in your Miata expects some resistance from the light bulbs. If that resistance isn't there, it will flash faster, like you have a blown bulb. That's a clear sign of someone who has replaced their LEDs but hasn't paid any attention to actual function. It's a little embarassing to see. The solution is to either add inline resistors or install an appropriate flasher. We like the second option, but it's your call.