I have the same generation Miata and did this same exact job last month. The only things you need are a spring compressor (you can rent one at most auto stores, like NAPA), a wrench set, a breaker bar, jack, and jack stands.

I'm not sure how much your struts were, but returning them and buying coilovers would make the job much easier. The coilovers come as a fully-assembled unit. So you only have to jack the car up, take the three nuts off at the top of the shock tower, take the shock bolt off of the back of the knuckle, pull out the shock/spring assembly, and then reinstall the bolts in reverse with the coilover in place. No spring/shock disassembly required at all. And with the coilovers, you can adjust the suspension height and stiffness, and it'll make the car handle (and look) much better.

If you absolutely want those struts put in, I may be able to help out. DM me.