There are many transmissions options and it all depends on what you want and what your skills and/or funds are. If you currently have a 3 speed trans it started out with a column shifter. The floor shifter has been added somewhere in it's life.
Your current configuration has the rear mounts located between the bellhousing and the crossmember. Any auto trans that you choose would have a mount near the rear of the trans. You would likely need to procure an aftermarket rear crossmember. You will need a flexplate, starter, either a new radiator with a built in trans cooler or a remote cooler and lines. Also, some sort of shift mechanism, and driveshaft modifications. Most current conversions involve a more modern overdrive trans such as a 700R4 or 2004R. However, there is nothing wrong with a 350 trans, it's just not an overdrive.
Fred

Last edited by rfs56trk; 11/06/2014 5:42 PM.

1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine