See
MPC Transmission -- Synchro Mesh (Typical 1956-57)
MPC Heavy Duty Transmission -- Synchro Mesh (Typical (1958-59)
1956 Shop Manual, Section 7
1957 Shop Manual, Section 7
The 1956-57 Pontiac Transmission is a heavy duty transmission, probably about as strong as any 3-speed transmission. This would be the best choice for ease of installation. It has considerable gear whine in first & second (similar to 55) and that's probably why it was discontinued. Personally, I find the gear whine desirable, music to my ears. You will need the 1957-57 bell housing for this transmission. Your standard transmission cross member will work and the motor mounts will bolt up without any modification. I suspect clutch linkage will bolt up but not certain. I don't know about shift linkage, you probably will need at least the shift rods from column to transmission. I don't know about internal steering column shift mechanism. A search in the
Master Parts Catalog will tell you what internal parts are the same/different. You would need the 1956-57 yoke so would probably have to modify your 55 drive shaft or use a 56/57 drive shaft. Your best bet would be to find a 56/57 parts car with the standard transmission. 57 would be better because you could use the stronger rear end and probably would have everything you need for bolt in installation, including the steering column if needed.
For the 1958-59 transmission, you will need the 1958-60 bell housing. You will need a different cross member, 1956 or 1957 Controlled Coupling Hydramatic cross member can be used by making a couple of simple adapters. I don't know about linkage issues you would run into. I don't see this as a good option for simple installation.
I have no idea about cost.