insofar as mustangs;
at the $5k price range I would consider the following
99-04 GT (265hp, has traction control, bit rougher mod path if more power is saught)
89-95 GT (yes across two chassis, but all have the 5.0L 215ish hp, but easy NA mods)
You might find a ratty 96-98 Cobra at that price point, 305 stock HP and the mod path for much more is difficult ($4k blower for 450hp)
the path I would take is camber plates, koni or bilstien shocks, a big front swaybar (addco), maybe H&R race or even super-race springs, and a panhard rod for the rear axle.
Plus a nice set of pads at least.
should be fun, capable, and not break the bank overmuch.
I know that my 97 cobra gets about 20mpg. You may also face having to rebuild the stock LSD every year or every other year ($70ish in parts) unless you upgrade to a torsen or other mechanical LSD type.
I also have a Miata and it is a better car for teaching than the mustang. The Miata is very precise and the lack of power makes mistakes show. The mustang has power to make mistakes less apparent, can get you in more trouble quickly if you dont respect it, and comparatively is a car you have to grab by the skruff of the neck and make it do what you are asking of it. That said, it makes fun V8 sounds and the power is cathardic.
Consumables are much cheaper on the Miata, price 205/50/15's (size my STS miata wears) vs 275/40/17 or 245/45/17 (the 275 is the 17x9 fitment and there isnt much in the way of great tires in that size)
As far as auto-x classing... you have STP and CAM to consider in addition to ESP with the additional savings of them being street tire classes.