There are those of us who believe that racing is fun in just about any car... and you may think you're one of us. But, you started out in a really fast car. Before you invest a bunch of money in a Spec Miata, spend some time with a Miata and see if it's right for you. It's a momentum car. Power is "adequate" in an old-school sportscar kind of way, but it's not gonna get up and go like you're used to. It takes a completely different driving style to get the most out of it.
$8k probably isn't too bad for a well-prepared SM. The absolute cheapest you could hack one together for would be $4-5k.
A Miata is good for about 12-15 mpg at Sebring.
A SM can be autocrossed, but it's probably not the best suspension choice for autocross. (I've heard that it's not the best choice for racing, either! But, it is what it is, and your competition has the same thing.) The front springs are SUPER stiff, and the spec shocks don't provide quite enough damping for them. You'd definitely have fun autocrossing it, though. You can't avoid having fun racing a Miata in any environment.
Explore all of your options. There's Spec Miata, Spec E30, etc. There are other options with SCCA/NASA/PBOC/Chin/Etc, as well. Spec racing is cheap "in theory". The reality is that it can be relatively cheap to get out there and race... but if you get the itch to win, WINNING ain't cheap.
Then there's the whole low-buck LeMons/Chump racing scene. You can build a LeMon for $3-4k and have a ton of fun racing for a lot less expense than anywhere else. Or, better still, you can scab onto an existing team (there are at least 6 active teams in the Tampa area that I know of, somebody always needs a driver) and skip the burden of owning a race car and a trailer and all the hassle that goes with it. Get 3-4 hours of wheel-to-wheel track time in a weekend for $700-1000. You can't beat that.