At least a 16" wheel, and preferably 17. Stock size tires on my LS1 Z28 was 245-50-16, so you probably want to stay close to that. When new, my car could ROAST the stock Goodyear Eagle GS-C's. 275-40-17's were much better for grip on race tracks. A big reason for bigger wheels is so you can put bigger front brakes on.
Hate to say it, but it sounds like you're stuck.
There's no way to get enough tire under a Miata to cope with the torque of an LS unless you're willing to go to a super-sticky compound -- which you don't want to do because you want half-decent tread life.
The tire that currently offers the best available combination of dry traction, wet traction, and usable tread life is the Michelin Pilot Super Sport; that's a non-starter because it doesn't come in 15" or 16" sizes.
Something's gotta give.
^^^Same reason we passed on a cherry perfect GTO last month in a fire sale situation. Absolutely a beautiful car but extremely limited by the wheel and tire thing.
Good luck to the OP, I know I'd want the best I could get under that flying squirrel...
My brother's NB 99 Miata has a couple sets of wheels.
15x9 TRMotorsports +36mm offset with 225/45R15 Hankook Ventus R-S3 (version 1)
- the slight stretch of the tire fits just fine under the NB's fenders and is nice and flush. Fantastic tire even in the rain. Longevity, well it's an extreme performance summer tire. Depending on how aggresive your alignment settings are, I don't see why you couldn't get 20k miles out of these considering how light the Miata is.
15x7 Kosei K1 +45mm with 205/50R15 Dunlop Z1 Star Specs.
- these were some of the best tires you could get for the Miata at the time he bought these. Since then, I've read that the BFG Rivals are better.
- the 45mm offset and 7" width (though not as flush as the 15x9 at 36mm) actually keeps this closer to stock steering angles, reducing the scrub radius effect/being jittery while steering over bumps (or whatever it is called, I can't recall the technical term at the moment).
My suggestion would be a set of 15x8 +20mm or 15x9 +36mm wheels, TRMotorsports (C1 for the 15x8 or the C3M for the 15x9) or the 9UL wheels, with a set of 225/45R15 BFG Rivals or the ver2 Hankook RS-3 tires. I'd leans more towards the 225/45 versus the 205/50 because you'll need as much grip as you can get with that much power. Although there is a fair bit more of tires to choose from in the 205/50, and possibly longer lasting, they are not going to provide as much of the needed grip as the 225/45. And as said before, depending on how aggressive you set your alignment is set (mainly the toe for turn in response) will be a big factor on how long the tires last (being that the insde edge will feather with more aggressive settings), unless you burn out on every straight