I think a good part of your decision making process is your proposed use of the car and what are the important points, above and beyond the styling. For example...
'65-66's are the "originals", as in the first couple years of the first "pony" car. They are pretty much "no frills" and unsophisticated (IMHO in a GOOD way) but may not be as attractive to prospective owners looking for a few more creature comforts/conveniences and/or safety features.
What '67-'68's will offer over '65-66's is a bit wider engine compartment, capable of housing the larger "FE" engines (390-428) and a few more conveniences and things like a much more refined factory air conditioner (didn't hang off the bottom of the dash like the earlier cars), snazzier trim, available in-dash tachometer, "turn-signal" hood, dual-circuit brake system, power front disc brakes, overhead console, etc. In addition, the '68's had a collapsible steering column, locking seat backs, shoulder belts, side-marker lamps, etc. There were even some '67-68's with factory cruise control, low fuel warning light, and more.
So, for someone who has comfort and safety in mind, a '68 might make more sense than a '65-67. For the "purist", a '65-66 might be the choice.
In terms of affordability, a hardtop will generally be the least expensive to purchase, a 2+2/fastback next and a convertible at the top, all similarly equipped. Conversely, a convertible will suffer the most from structural issues due to rust and maintenance of the soft top and mechanism, the hardtop and fastback having a little more structural integrity due to the metal roof structure.
From a performance vs. economy standpoint you go from the small six (170 in early '65, 200 in later models) to the small V8's (260 in '65, 289 in '65-68 and 302 in '68) to the "big iron" in '67-68 (390). Various configurations abound between the V8 models from 2V to 4V carburetion and "High Performance" in the 289 from '65-67. Generally speaking, the small six and 2V V8's offer better fuel mileage than the 4V engines and manual transmissions give better mileage than automatics.
As all Mustangs are of unitized construction (unibody) where the body and frame are combined in the same unit, corrosion due to rust can be a significant issue. Cars that have been driven in winter road salt or very close to the seacoast are the first to suffer. The cars from the "rust belt" will typically have problems in the subframe rails, floors and floor supports, rocker panels, torque boxes, trunk drop-offs, lower front fenders, lower doors and lower quarter panels and cars around the seacoast, especially HUMID areas will have rust in the cowls, sail panels, rear window filler panel, hood and trunk edges, windshield pillars, roof drip rails, etc.
If you're serious about looking for a vintage Mustang then I'd first get involved with a vintage Mustang club or organization that has a local presence and get to know other owners and get a new friend to go with you to evaluate prospective purchases.
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Welcome to the addiction and good luck!