Hello! I would start with some greetings like "Buenos días (Good day)" or courtesy expressions like "por favor" (please). Even though you may not be fluent, making the effort to speak to locals in their language has a tremendously positive effect and they'll want to be helpful back. The next area I would learn is for getting a taxi, giving an address, and ordering food. If you're shopping, you can learn a phrase or two like "Cuánto cuesta"(How much does it cost?) or "Dónde hay una zapatería" (Where is there a shoe store?).
Another thing to keep in mind when shopping at smaller local stores in Mexico and some other parts of Latin America, is that there usually is some haggling over price. Be prepared to ask for a lower price, so knowing some basic numbers and the exchange rate is also great. I hope that helps. ¡Buen viaje!