Welcome to the forum from North Carolina.
Looks like you have picked a good bone to start with. I would rather have a car that has never been painted than a shiny one full of filler and rust.
There are a few areas on these cars that are prone to rust. They never dipped these cars in primer. They did get two coats of epoxy primer. Depending on how early your car was might be red oxide primer but if built in Dearborn will be gray.
Areas to look at for rust.
#1: The cowl at base of windshield. The windshield lays on the cowl and there is a gap between the glass and metal. Trash collects in there and so rust is likely.
#2: Inside the cowl on an AC car you have only one opening going into the cabin that is above the heater box on the R.H. side. Mice, chipmunks and such love to build nests inside the cowl and the heater box. To stop them when you have rebuilt your car you need to add mesh wire under the cowl vents and between the cowl and heater box. You can look inside the car at the bottom of the cowl and if you see water marks or rust you have rust holes in the cowl. Simply washing the car causes this to happen.
#3: Rust around the tail lights. The tail lights bolt in from the inside and have a soft rubber gasket. There is a space that holds water and again simply washing the car causes rust. They did not do a good job spraying paint on the inside.
#4: Trunk floor and drop off to the quarter panels. This holds water if the tail lights leak and so feeds the rust.
#5: You should pull the interior out and look for your build sheet during the process. I have seen under the carpet, under the sound deadening, stuffed into the back seat springs, also stuffed in the seat riser welded to the floor. This sheet tells you everything used to assembly your car down the line.
Now that you have the interior out if the cowl has leaked it eats up the front floors. If you have leaks from the vinyl roof then rear floors and under seat will rust.
#6: On vinyl roof cars Ford did not spray top coats of color on the roof only the primer so not much protection. Leaks start around the holes for the fasteners and clips and the rust begins to creep out. Also around the rear windows and roof rails are subject to holding water and spreading the rust.
Your car looks correct for the vinyl roof. You can order a Marti report to get all the details on your car.
One thing on your car is the Protection Group. That is the side strips, and I think the bumper guards were part of that in 71. Not sure if you got the locking spare tire in 71 I think not. I need the side strips if you are going to leave them off the build.
Now to get one of these to handle you have the right engine. The 302 is the lightest of the V-8s that were available. You can get lots of power out of it tons of SMF performance items out there.
The chassis on these of course flexes, all do even your M. You can add sub frame connectors, better springs and shocks, different front upper and lower control arms, drop spindles, roll cage. Just depends on how serious you want to get.
Holman Moody took a unitized body Fairlane and won a class at LaMans in 1965 I believe. You can make any car handle with the right parts. The modifications to the Shelby Mustangs were developed by Holman Moody also. Simple, easy to do and not expensive.
When you start to take the car apart do not think you can just go buy and new part. Some parts are not available so be careful and take lots of pics and bag and tag everything.
The coupe will make the best handling of the three bodies due to having a shorter roof than the fastback and is probably stiffer.
I was building a convertible for track days I figured that no top lowered the center of gravity and would be better. Roll cage is required so that would stiffen it right up.
Here is link to video and sound of a SBF on the track. Not many engines sound this good.
Hope it works I get it right some times, lol.
BTW my son is head inspector at the BMW plant in Spartanburg, S.C. he is on the six line. He said he would never buy a BMW they have so many quality issues, lol. He drives a 2018 GT Mustang. At one time BMW hired a bunch of Jack Roush's mechanics to come to BMW and work in the plant to do repairs. They had over 5,000 cars in the lot that needed to come back into the plant and be fixed. They actually crush some cars that they cannot figure out what is wrong when brand new. If you knew the profit margin on a BMW you would pass out. $14,000 for and X-6 out the door.