simple build you want to be auto canceling your 3 late game when fighting enemy back line to squeeze out the most damage in the shortest amount of time. high strength build with items that synergies strongly with lokis auto attack cancel. you should always start your 3, then level your 2, then your 1 in that order, but youre usually maxing your 1 since it applies the damage on the enemy which can persists through global ults like apollo.
beads/aegis typically depends on the type of cc their support has. long stuns like ymir freeze or pulls like xing/ares ult beads is much better. aegis helps vs gods with execute like thana and achilles or high burst damage characters like janus. beads is usually more useful though.
i dont think this matters much i prefer the reaper because of the passive and pen but barbed carver has strong synergy with lokis ability. i think its preference because you do so much damage to squishes the carver procs aren't always necessary.