Monkeyboy -Without going into too much detail, a 1965 Mustang GT could have been any of the 3 body styles (including 2+2 or "fastback" as they are more commonly called).
It was essentially an appearance and performance package that could be ordered begining in April of 1965. It included.
A-code challenger 289 or K-code Hi Performance 289 V8s
Disc brakes (manual only)
Dual Exhaust with special louvered "trumpet" tips that exit thru the rear valance
Handling suspension package
Quarter ornament (fake scoop on flank) and rocker molding delete
GT side stripes
Grille-mounted fog lamps
Shelby took K-code (hi-performance 289) 65 fastbacks and modified the engine, suspension and tires to an even higher standard. Carroll Shelby himself (thru his company, Shelby American) modified fastback Mustangs from 1965 thru 1967 and these cars, as you guessed, are quite rare and very expensive. They are very close to race cars that were licensable as a street car - especially the 65s.
Just about all of the special equipment Shelby added to these cars is being reproduced today and many people take garden-variety Mustang fastbackss and modify them to look and perform like an early Shelby GT350. These are called "clones".
In 1968 Ford assumed responsibility for production of Shelby Mustangs and expanded the lineup to include convertible. With each successive year, the cars moved further away from their racing heritage. The last year Ford built Shelby Mustangs was 1970, and those were actually leftover 1969 models.
The GT500s were 428 police interceptor powered 67 (first year) Mustangs modified by Shelby. Due in part to the movie "Gone in 60 Seconds", these cars have become wildly popular and even more valuable than they were. They are not affordable for most of us.
Hope that answers your questions.