A new Starting weapon screen on the main menu lets you choose the weapon you begin each run with.
Two new starting weapons are hidden at first. Each has its own unlock challenge, shown on the Starting weapon screen; once unlocked, you buy it with souls.
Each new weapon replaces your darts for the whole run and comes with its own upgrade cards.
The second weapon's challenge only appears once you've unlocked the first.
Demo
The demo shows the Starting weapon screen; the new weapons are in the full game.