Welcome. It sounds like you have decent tires already, so for your first real road course outing I would put a new set of brake pads on it. For combined street and road course you could go with Hawk "Black" or "Blue". The black pads will be easier on your rotors. These cars have too little rear braking, so blue in back and black in front is a good combination (blue has more torque). Be sure to do a few additional things.
1) Bleed the brakes with new fluid (Motul RBF 600 is great).
2) Get rid of the stock rubber brake lines in front. They can melt and fail if they get too hot, spewing brake fluid all over the track (not good) and putting you and everyone else in great danger. Many clubs will not allow your car to pass tech inspection with the stock hoses up front. Goodridge makes excellent braided SS hoses that are easy to install.
3) You'll undoubtedly need a newer SA rated helmet. Some clubs allow M rated, but many don't. Find out first before you show up.
4) Change your oil and consider running 1/2 to 1 quart extra. That helps avoid loss of oil pressure in the turns.
I agree that a panhard bar in back is needed. That rear suspension you have now dates back to the 1977 Ford Fairmont. If you run it on a road course you'll probably see the rear tires rubbing on the tailpipes. That means your rear axle is moving back and forth laterally at least 6 inches (probably more like 7 inches). Yes... it's that bad. Don't waste your time with upgraded control arms in back. That rear suspension is designed to bind when articulated. That's why Ford put such flimsy control arms back there. Stiffer arms in back just mean more binding. Consider contacting Griggs Racing (griggsracing.com) or Maximum Motorsports. Griggs is the best, but MM is less expensive. My Cobra R has Griggs' full World Challenge frame and suspension setup with no rubber or polyurethane bushings anywhere, it's all Heim jointed now.
Many clubs have a driving school in the spring, so consider signing up for that. I did, and I put my son through it as well. They usually team newbies up with a highly experienced driver that can really help coach you on things like late apex of corners, brake points, etc. An autocross, as others have mentioned, is also not a bad idea. You will get your butt kicked by those pesky Miatas. Don't let that bother or discourage you. Mustangs aren't great autocross cars no matter what you do to them. Road course yes, autocross not so much.
Best of luck. CobraRGuy