The core loop: dying makes you stronger
Death is not a penalty in +1 DMG Per Revive — when your character dies, it revives and permanently gains attack damage, which is where the game's name comes from. This death-to-revive cycle is the core progression loop the game is built around, according to Destructoid and Pro Game Guides.
Leveling adds a separate damage bonus
Every character level grants +1% Attack Damage, according to gamestratwiki's breakdown of the leveling system. This stacks on top of whatever bonus you get from the revive loop itself, so leveling up between deaths is worth doing rather than skipping.
The Reaper speeds up your revive cycle
The Reaper is a mechanic that follows your character and cuts your max HP in half, which sounds bad but actually shortens the time between deaths, letting you loop through the revive bonus faster, per gamestratwiki. The Reaper Follow gamepass keeps the Reaper attached permanently instead of losing it between runs.
What to prioritize early
Check the codes page before your first session, since active codes hand out Death Coins and Soul Rings that go further early than later. Beyond that, gamestratwiki's own early-game sequence names one explicit build priority: equip Vengeance whenever possible, since it's the ring most directly tied to progression. See the First 30 Minutes guide for the full step-by-step order gamestratwiki recommends.