Unless the transmission has been changed, the factory transmission would be an SM318 Muncie 3 speed. It is easily identified as having a 4 bolt side cover. A later Saganaw full syncro 3 speed would have a 7 bolt side cover and would have been sourced from a 67 up vehicle. You should be able to find a factory repair manual online on this site or purchase one from several aftermarket suppliers.
Replacement of the the 3 speed transmission with a 4 speed would require a completely different driveshaft and a replacement floorboard as the 4 speed is taller. I don't see any advantage to going in this direction unless nothing else is available. If all the current transmission needs is bearings, they are available from a number of sources. The front bearing number is 6207 and the rear is 6306.
Fred


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