Car trannies will have all four mounting bolts from the outside, where the truck ones have the top two on the outside and the bottom two from the inside. If you use a car tranny with a truck bellhousing, you need to use a bolt and nut on the bottom two.
55-57 car and 55-63 truck are interchangeable, except for the mounting holes, and possibly the side cover, which you can reuse from your old one if necessary.
I've used a floor shifter with the above trannies before. The arms can be flipped. A "U" bolt and an "L" shaped bracket is all there is to it. The bracket can be bolted on in either position. Aftermarket shifters come with everything you need to do this anyway.