Farmer's Fury

Typically, I find it best to prioritize both penetration and cooldowns with Persephone. Because she has a slow start; having those quick cooldowns helps with snowballing with Persephone and in return making you very powerful in a short amount of time.
I recommend having those four being base, yet still having in mind the enemy's build. Typically anti-heal is always swapped within my build but in the rare occasion that I don't need it, using spear of magus is spicy for my build.
For most of my games I destroy and conquer with this build alone, however with tanky enemy teams I recommend using ethereal staff and building Charon's coin after Chrono's pendant and building that with obsidian shard for extra tank destroyer.
If you wanna build life steal soul gem and spear of magus would be my recommendation.

For relics, I'm confident in my skill, so I enjoy using a blink ruin to get places faster when my team is pushing; always have to use your ultimate in team fights. With that said, purification beads comes in handy a lot, so does aegis, however I rarely use it.
A trick to keep in mind, both aegis and beads look the same when used, typically you can pop beads and people will think it's aegis so you can get away with just running beads.