A tape measure is your friend. Shoeboxes are some what smaller than the 1960s full-size. They have the same weight as midsized cars like Fairlanes, Chevelles, Lemans...stuff like that. Mid 60s TBirds seem to be more midsize compared to the 61-63 bodies. Shoeboxes are narrow, not quite as narrow as a 40's car, but seat width is where you'll have trouble. Keep (if you have it) the stock seat frame and springs as you may want to recover one day. The floor under the seat is flat. The transmission hump is minimal. You may have to drill new holes for the new seat frame but it's about as straight forward as you can get.
I just measured my '51 and a '66 T-Bird. They are both close to 57 inches inside. There is a '64 Bird being scrapped here and I like the interior. If it fits even close I will let others know.
I've got 65 T-Bird seats in my 46 coupe so you should be able to get them in a 51. Seat back takes some planning.
You don't have to go very far in the early Hot Rod mags to see many examples of it done. As for what it takes it will very from one Guy to another. Making them fit and look good has to do with your skills more than actual size. For some it's just the size of there Wallet.
If the body is narrower you are leaving out the console so width should not be a problem. You may have to raise the seats up on blocks to see out the windows. Get the seats with seat tracks, then you only need to drill some holes and bolt them down. Unless they are electric, then you need to wire them up. In that case go by the factory T bird wiring diagram.
Fits great in my '49 Merc. Not sure if the width is different from Ford to Merc. The fronts would be no problem. If the rear is a little too wide, it would be easy enough to section the rear lower down the middle, and leave the armrest out of the back. You could make any size panel between the backrests. If you use the package tray, that would need to be sectioned as well.