I'm 35 so I don't pay anywhere near what you will have to pay but Miata insurance should be pretty reasonable. It has a low theft rate, repairs are less expensive than most cars, on paper the car stats appear benign. (4 cyl with a tad over 100hp) and unlike a WRX, Miatas have a good rep of safety/low accident rate with the insurance companies.
Call some Insurance companies and get some quotes. Remember to compare apples to apples and get quotes for the EXACT same levels of coverage. Since you have a clean record, I'd stick with a major carrier like State Farm, Farmers, USAA, etc. even if you end up paying a little bit more. They're worth it if you ever need them.
Also, look for discounts like A student, automatic payments and additional insurance discounts. Get Homeowner or Renter insurance and a life insurance policy with the same carrier and you can save big $$$. The life insurance for a 18yo would be cheap and the premiums may be a wash with the discount.
As for the full coverage, realize insurance companies will only reimburse on resale value and make little to no consideration for mods. If you have a lein on the car you will need to carry full coverage. If you own the car outright, the choice is yours.
If totalling the car would put you in a huge bind but you can afford the premiums of full coverage then get it. If not, take your chances with basic liability. Sock the savings away into the bank so if you do wreck your car, you have $$$ set aside just in case.