There are similarties and differances between the 53-62 full pressure 235s.
Similarities: All 53-62 FP 235s use 2.150" front cam bearings, so any mech cam will work in any 53-62 235. The 53-55 1st 235s used a mech lifter that had a "cup" on top that used a shorter push rod. Don't know what the hyd lifter or pushrods looked like for 53-55. All lifter diameters are the same, so no problem there.
Differances: The 53-57 blocks were not all drilled for hyd lifters. Only the powerglide units had hyd lifters in sedans until '57-58. Then I think most 235s got drilled for hyd, even if solids were used. I've only seen the fiber cam gear, but some guys here say that the cam gear was metal in truck engines.
I think all '55-62 pushrods are the same length for both solid and hyd applications. The '55-62 solids can be used in any '53-62 engine with a mechanical cam and the '55-62 pushrods. You must make sure that the solid lifters have the "groove" cut into their body to let oil flow around them if used in an engine that does not have the oil line in the pushrod galley.
Short answer: It is OK to use '55-62 solid lifters and tubular pushrods in a '53-55 1st engine, provided they are used with a mechanical camshaft. Make sure to use the oil line internal to the pushrod cover, with the proper oil restrictor.
The hyd lifters can rattle during highway operation due to poor oil supply, valvetrain geometery and valvetrain weight/spring pressure.
What you cannot/must do:
Do not use a hyd cam or lifters in an engine not drilled for hyd lifters.
You cannot run hyd lifters on a solid cam.
You cannot run solid lifters on a hyd cam.
You cannot reuse lifters on another cam.
You must keep lifters in order when swapping used cam & lifters between engines.
The '53 PG sedan engine was the first full pressure engine, featuring cast aluminum pistons, new cyl head, higher CR, bigger intake, shim-type main bearings, insert rod bearings, full oil pressure & passages, bigger cam bearings, improved valvetrain. It was carried over in the '54 stick sedans. The '54 PG engines got hyd lifters and a slightly hotter camshaft. Now I don't know for sure, but I have read from several sources and Motor's Manuals that some, if not all, 53 PG engines had solid lifters, but can't say from personal experience. Your results may vary.
good luck
chip