If you are invited to a picnic or a tour of the country side, dress casually, but elegantly. Polo style shirts, a sweater and sporty slacks would do. Business meals are the time to get to know each other, conversation may wander through many different topics. Breakfasts are also the preferred choice to meet, get to know, and exchange information over the potential business deal. It is impolite to split the bill.
Lunches are an integral part of business in Mexico.
Ironically, though, business will rarely come up during those lunches. The occasion will be used mainly as a means of getting to know you. Whatever you do, don't ruin the mood by pulling papers out of your briefcase for discussion or review. Business may be the intention, but overall it will be much more subtle. Fax machines are also very common.