A couple of clarifications here:
Indeed, this is a 1950 Nash Rambler Custom Convertible. The convertible was the first bodystyle introduced for the 1950 model year but a two-door wagon joined the lineup about halfway through the year.
The engine is Nash's 173 cubic inch flathead six, introduced in the 1941 Ambassador 600. Nash and AMC stuck with variations on this engine right through the end in '88. It is indestructible and efficient.
This, like all Nashes of the period (though not Hudsons) is a true unibody using only sheet metal gussets to form the structure. As such, rust is a killer. It's possible this car is salvageable but it's a project for a skilled metal worker. That being said, they are not at all common. 9000 produced may not be "rare" but there aren't many survivors.
I'd suggest anyone with interest in this car to seek out the Nash Car Club of America. There are several enthusiastic owners of first generation Ramblers that would be happy to give you pointers!