Hooo Boy...
A smile and authentic "Buenas....." will buy more respect and help than an indifferent attitude and 100,000 word vocabulary.
Want peanut butter, crema de cacahuates? Simply ask Jif? Skippy? with a smile. Want salad dressing? Say "salad" with your hand making a bottle shaking over a bowl motion. Soup? Campbells. Steak? T-Bone,
The book. The People's Guide to Mexico by Carl Franz has more info in it and is a great read. Not a guidebook, it's HOW to travel Mexico not where to go. Lots of shopping and traveling expressions.
The enthusiastic help, coaching and prompting Mexicans offer a non Spanish Speaker is one of the endearing memories a person will take home.
Stuff self-consciousness in a drawer and leave it at home.
For years I lived in Indian communities in guerrero and oaxaca where few spoke even basic spanish never mind english.