According to Patrick's catalog, solid lifters came with every stick transmission vehicle between 1950 & 1957 with either 216, 235 or 261. Hydraulics only came with Powerglide cars. If you use the 55 bellhousing you will no longer have the bellhousing side mounts like the 51. If you want to use a more modern tranny, use a bellhousing from a 48 - 53 truck (it will have side mounts like the 51). You got to have bellhousing mounts if you maintain the front engine mounts. Also note the early bellhousings have the cultch linkage coming out at an angle. I'm not sure the truck bellhousing has the angle clutch linkage. Perhaps another inliner can advise. Get a saginaw from a 66 - 77 Impala (3 speed). It will have full syncro & will bolt up to the truck bellhousing.
To put the 55 into your 51, you will need to install the front plate off the 51 216 on the 55 235. The cam hole on the 216 front plate will need to be drilled out from 2 & 1/4" to 2 & 3/8". I know in 54 the cam hole was increased to the larger size. To remove or install front plates, you need to pull the cam out.
Another option is to keep the original 3 speed, but get a torque tube rear out of a early Powerglide car. It will have a more desirable 3:55 gear instead of the manual 4:11 gear. That way you could do some highway driving. This is an all bolt in change.
I have a 51 sedan which I am planning on installing a 62 235. I picked up a boneyard 5 speed T5 from a 87 S10 truck (last year for mechanical speedo). Buffalo Steve makes an adapter plate to match the T5 to the 51 bellhousing. The clutch throw out bearing sleeve on the front of tranny also needs to be shortened by Buffalo. The 3:76 1st gear tranny is best for the 235 along with a S10 4x4 rear with a ratio 3:73. You need the 4x4 rear as it is wider than 2wd & is almost exactly the same width as the original rear. You will need leaf springs from Buffalo. With this combo, you should be able to drive 70 mph in 5th gear at 2500 rpm with nominal tire size. The crossmember on your 51 will need to be cut & the rear of the T5 supported by angle iron (Buffalo has the details).
Hope this helps.
Sherman