I really liked Digimon World for PS1. I sort of want to dig out my copy and play it. It would mostly consist of me making my Digimon eat its own poops -- which you can do in that game -- but that's okay.
Digimon Story Cyber Sleuth probably doesn't let you let your pets eat their poops. You'll also probably never play it because its Japanese.
Instead, go watch Summer Wars. It's the Digimon Movie (because it's the same director), but actually good (because ???).