Pushrod selection

Cut your oil filter open and see what is in there. A plugging oil filter will start rattling the lifters after it has been run for a bit.

Prime example of particles of old gaskets or whatever in your oil pan (or crud) getting sucked up into the oil pickup screen after it has run for a bit.

If lifters start rattling after they have been started up running quiet, it means that the lifter feed is loosing it's oil pressure and can no longer pump up the lifters . . so they bleed back down and start to rattle.