Sidehill welcome to Stovebolt. You have found a good spot with good people and generally good information (except politics) when you found this place!
With GMC identification, it all starts with the serial number, which can be found on the driver's doorpost ID plate. 250 is a one ton truck, not a 1.5 ton which is a 300 series. (280 is a 1.25 ton)
A '51 one ton shortbed would have a serial number on the Doorpost ID plate that would read 251 22 P _ _ _ _ _ or similar.
Wheelbase ID is the 3rd digit:
1 = 116"
2 = 125.25"
3 = 137"
I have never seen any GMC one tons other than 137" but I know that they are out there...somewhere.
If it's a 3/4 ton the number will be 152 22 P _ _ _ _ . First two digits are the series and rating.
The 3/4 ton stock rear was 4.57:1 and the optional was 5.14:1. The one ton stock rear was 5.14:1. The 3/4 ton rims are 15" split rims as stock, and 17" split rims optional. The One ton has 700-17 tires stock and 700-18 tires optional both on split rims.
The SM420 four speed tranny was the same one that was used for close 25 years so yup, it is the same as your '53 3/4 ton most likely.