Tough to limit it to just 3. I have more than 3 that I grew up using and enjoy with Asian foods:
1) Huy Fung Chili Garlic Sauce
2) Huy Fung Sriracha
3) AGV Sweet Chili Sauce
For Mexican (and most other Latino) food (excluding salsas), I prefer:
1) El Yucateco XXXtra Hot
2) Tapatio
3) Cholula
I'm not fond of sour foods, which includes vinegar-forward hot sauces, which includes most American hot sauces. Of American hot sauces, I prefer Tabasco Chipotle. That said, I've not tried many American hot sauces (again, I don't like vinegar-forward hot sauces).