This may sound like a dumb question. What will be the purpose of the car? If it's climb in and drive it, by the way a Mustang would be neat, I don't recomend it or any other vintage car.
When a 71 Cadillac or Mercedes was brand new their reliability maybe slightly but not a whole lot better than a Mustang or Camero. Even low priced recent cars are very reliable. It's like going to a French restuarant...if you have to ask the price you shouldn't be there (did it once...wow!). By the way cars since 1990 almost all have electronic fuel injection and ignition. You turn the key, it starts and off you go. Tune up may be needed every 90,000 miles!
If you ask about gas mileage chances are you'll be disappointed. 15-20 mpg is normal whereas on recent cars 25-35 mpg is normal.
I've owned my 68 Mustang for 35 years. It has been very reliable in my opinion but I always tinkered with it because that's always been my hobby.
I got my first car when I was in high school. Had a part time job at a service station and most of my spare time was working on that car and/or other's car. Spent some time here and there for college degree, wife, kids and building house but cars have always been my hobby.
You and your parents need to consider if a vintage car is for you at this time in your life. In my opinion bringing a mechanic and/or a vintage car person along is secondary to making the right decision.
To be practical...strange for a car nut... you can get a really great condition used recent car for less than $10,000 (most I've spent is $7000). Recent cars 90,000 is the mileage for their first major service. 200,000 is assumed no problem!
Hey, I love Stangs, kills me to say all this but it's kinda like marriage. It's a lot more than a pretty girl...
Safety. The 71-73 is probably the safest of the vintage Mustangs. With that in mind they have little of what now is assumed on a car: Air bags, ABS, Traction control etc. Rear wheel drive can be an experience if you're used to front wheel drive.
My '64 1/2 vert. Ordered May '64. D code 4 speed, handling package, caspian blue, accent group, Ford blue manual top.
'68 vert. driver. Owned since Apr '78. C code AT, AC, PS, P disc B, PT lime gold, standard black interior and top. NOS RF fender and left quarter.New top and folding glass.