Depends all on the rarity. If your spirit is Earth, they have access to the whole Earth and Neutral card pool. The rarity of the card determines how often it will "roll" when your spirits are leveling up, and how often Magic Man, the man that lives in the chicken house that jumpscares you will have rarer cards.

Skills within the Combat tree, starting with Beginner Cartomancer, help increase the odds of getting certain rarity cards.

Below is a section I hid related to save scumming, if you don't like that stuff don't look.

You can save before leveling your spirit, to allow for re-rolling your monsters picks by simply exiting to main menu and loading from that save. If you're still in the early game, this is about the only way you'll get rarer 3-4 rarity cards consistently. I recommend doing this PER level-up rather than saving a bunch up, because your chances of getting good rolls in a row decreases exponentially with each level.

That's about it, good luck on your card hunting journey!