Although teachers say there are only two agile project management methodologies - Kanban and Scrum, I've counted several more, and anyone who googles can find an endless number of variations. But I've identified 6 methodologies in total (in the picture). Among them, 1 is chaos (no methodology), 1 is non-agile (waterfall), and 4 are agile.
Which one do we choose for a startup?

If you're just starting out, with a team of 2-3 people, the best choice might surprise you - it's Chaos, i.e., not using any methodology. Why? Any methodology requires spending time on non-value-adding maintenance - going through rituals, creating templates, implementation, choosing tools, etc. This is not needed at the start, especially for a small team. Act in chaos, and your pool of actions will tell you which tools you need.

If you have a team of 5 or more, you've already made the first prototypes and are starting to enter a steady development process, and you feel you're beginning to lose tasks and control - it's time to adopt and implement agile project management methodologies.

And waterfall is not for startups at all, don't even look in its direction - you'll need it when you have a serious operations or executive director - they will implement it then.