Hypereutectic pistons are a good balance between cost and durability.
You should look also at physically descaling the block before handing it to the rebuilders - remove all plugs yourself, and dig out as much scale as you can get with long screwdrivers. Now have the block hot tanked, and roughly bored.
Go with the minimum overbore, and have it torque plate honed. Finding a shop to do this part, is not so easy.
Get the crank reground or linished, and have your flywheel refaced. Also check your balancer (damper) and either rebuild or re-use. Rods may be closed and honed. The pistons, rods, crank, flywheel and damper are now subjected to first static, then dynamic balancing. Pistons are fitted onto the rods. Remember that with the hone-to-fit, each specific piston "belongs" to a certain bore.
Mock up the block and crank, with pistons/rods for #1 and #6 fitted (no rings). The metal between your bearing backs and the block, is to be bone dry - no oil whatsoever. Check your deck height, then tear down again and deck the block. You can use this mock-up, as a good time to test bearing clearances with Plastigage.
Now clean and deburr that block for most of a day. Don't forget all the bolt holes need chasing (preferably with chasing taps, not thread cutting taps) and to clean the oil galleries. I wash the bores last, as when you're rinsing them out, rust spots develop in seconds - wipe dry with paper towel and immediately oil the bores with a hand-wiping of motor oil. Fit the plugs for oil gallery and coolant, at either end of the block before mounting on the assembly stand. I suggest a light smear of Permatex #3 on each type, when installing.
Remove the old pilot bushing before the crank is refitted. Bearing shells are pressed in dry to block and caps as noted above; be aware that sometimes there are tiny shavings of metal from this process, that you need to dab up.
Apply a modest amount of either break-in oil or assembly lube to each main journal, sit the crank in place and finger-tighten your main cap bolts. Offset the rear main bearing oil seal halves by 1/32 and put the tiniest dab of gasket sealant on the mating faces of each seal half. Put a light smear of motor oil on each main cap bolt thread, and torque all to gently snug before final torque is applied to any. After torquing, check rotation is totally free.
Give the pistons/rods a quick "hose" with solvent to rinse away any honing grit or other contaminants on the outside. Make sure the gudgeon pins are well-oiled with either heavy oil or break-in lube.
Fit the piston rings, taking care to get the gaps sized, gap positions correct and rings the right way up (don't laugh too hard - it's a common mistake). As you did for the main bearings, make sure the shells are pressed against perfectly clean and dry metal, and crankpins lubed. Install piston assemblies one at a time, making sure the rod or rod bolts don't mar the bore or crankpins as the assembly slides down into place.
When all are torqued up to spec (oil on the threads, as for main caps), rotate the crankshaft a couple of dozen times in the normal direction. This will help bed in the crankshaft oil seal.
Pretty much everything else is as the many available manuals cover it, but the few variations above will get a more accurate (efficient) or reliable motor...