You probably won't buy the first car you see, don't let excitement get the best of you. Buy the car in the best condition you can afford, it will put you leaps ahead. I don't weld either so my main focus was frame rails, floor pan, trunk, cowl area. I eventually found a coupe after looking at >6 coupes and convertibles. The conversion from auto to stick isn't that involved from what I've read> pedals, Z bar and working around the exh. if headers. There are lots of upgrades to make it a nicer stick like 5sp. (OD is awesome), cable or hyd. activation vs. the Zbar manual linkage, etc.
I looked in the cowl with a flash light to check for heavy rust, this part does not come apart or off the car w/o drilling out many (>50?) welds and is an $$ fix. I layed on the ground and stuck my findgers into every opening under the floor pan I could find to see if I could dig out any rust scale, I did on the first 6 easily and passed on them. Open the trunk, look around where the gas tank mounts for rust as this is where water sits when the trunk seal leaks.
Unless you're doing a concours resto ask here or another forum what your options are before replacing anything, for example the '65-'68 16 gal. gas tank can be replaced with the '70 22 gal. tank with a little tweaking of the filler neck, costs no more than the smaller tank and only raises the top of the tank 1"-2" in the trunk. Without a lot of research or question asking you could waste money on replacements.
I would join your local Mustang club and go to a meeting, meet a member with a '65 fastback and crawl over the car with them, where to look, what to look for, someone may also be selling or know someone selling...car shows and cruise ins are a good place to meet owners also.
Jon