To add to former posts, new nuts and big end bolts are desirable but pricey. Existing Bolts are probably OK for further use, it depends on the nuts previously used, some locking types ruin the thread for further use. The problem with new ones are that many are not up to the job, even from trusted suppliers. As ironhead recommends, get the big end eyes checked for ovality. Any machine shop can do this.
The basic weakness in the design is the oil feed to the big ends, using the timing side bush to feed oil into the crank. The bush needs to have a good seal around the periphery where it mounts into the crankcase, a leak here will vent oil, rather than it going into the crank. Wear on the bush and crank journal will also reduce the oil to the big ends. Suggested running clearance here when new is 1-1.5 Thou. Plenty on the forum about this bush, choices, modifications, installation, sizing.
The sludge trap on your later crank is a removable tube. Folks take out the plugs, clean the hole they can see, leaving sludge on the outside of the tube. Remove the flywheel radial bolt and the tube will come out, revealing more sludge. The radial bolt should be replaced with a new one, Loctited in place for security, as a failure here wrecks the motor.
The wear limit on the journals is 2 Thou, they usually wear oval, so measure diameter in several places, and each side for taper. If the big end journals are reground, remove the sharp edge around the oil feed holes, blending them into the journal surface, otherwise they can cut a neat groove in your new shells. Con rods are the same forging, drive side/clutch side one has a small bleed hole from the big end eye, this should face to the flywheel, putting the bearing shell tab slots on the rods towards the front of the engine.
Pistons and rings.... Hepolite pistons, now distributed by Wassell, and only related by name to the originals, have yet to establish themselves as a viable alternative, so are best avoided. New old stock AE/Hepolite are OK, they were the standard when the bikes were new. Gandini rings have a good reputation, curing oiling and smoke problems when fitted to pistons otherwise considered to be at fault. In your part of the world, Hastings rings would be a good choice.
The small ball in the valve on the scavenge pipe in the sump needs to have reasonable movement, the ball often gets stuck by carbon and sludge, and the pipe needs to be secure and sealed into the crankcase.
BSA Service sheets are available in the Literature Section of the forum.
Good stuff there from birthday boy Musky.
Swarfy.