Just beginning

Of the cars you mentioned, the '71-'73 Mustang coupe would be inexpensive, fairly simple, and easy to find parts for.  A Sportsroof, Mach 1, or convertible will cost significantly more upfront.  A '67 T-Bird would be fairly inexpensive, but parts availability is worse and the car itself will be more complex, simply because they usually had more options to begin with.  '67 Cougars are neat, but I've noticed that prices seem to be inching up on those.  

The Club defines CCCA Classics or Full Classic™ Cars as:

"...fine or unusual motor cars which were built between and including the years 1915 to 1948. (Some cars /series  recognized by the Club are currently being accepted/considered on a "Please Apply" basis due to custom coachwork etc ). All of these are very special cars which are distinguished by their respective fine design, high engineering standards and superior workmanship."

https://www.classiccarclub.org/approved-classics

RozzoDec 24, 2020

Just retired and interested in the hobby. I like 71-73 Mustangs and 67 Thunderbirds/Cougars. With that in mind what is a good starter car assuming the restoration is not too complicated?

I do not think any "Classic"  CCCA car would fit into your category.  They are all good cars but none of them would be considered uncomplicated.

You could probably get excellent advise if you posted on the GM, Ford or Chrysler pages further down.

https://forums.aaca.org/forum/46-cadillac-lasalle/

https://forums.aaca.org/forum/57-buick-post-war/

https://forums.aaca.org/forum/37-ford-edsel-mercury-1954-and-newer/

https://forums.aaca.org/forum/40-chrysler-products-general/

I am sure you can get enough information here to be able to make an educated purchase.  Aaron has already provided information and these other fora will put you in touch with collectors/owners/restorers of POST WAR vehicles.

Good Luck in your search and happy hobbying.