The Shulhan Aruch (Orah Haim 211) presents the guidelines regarding the proper sequence to follow when one eats foods of different types, that require different Berachot. These Halachot are especially complex, but the basic rules are as follows:
1) If one is eating bread, then he recites the Beracha of "Ha’mosi" over the bread before eating any other foods. If one is eating different kinds of bread, made from different kinds of grain, then he recites the Beracha over bread made from wheat. If none of the breads are made from the wheat, then the order of precedence is barley, spelt, rye and then oats.
2) If one is not eating bread, but he eats "Mezonot" food, he first recites "Mezonot" and partakes of that food before reciting a Beracha on the other food. If one eats both rice and standard "Mezonot" food (such as crackers, cookies or cake), then the standard "Mezonot" food precedes the rice.
3) If one is eating several different fruits among the special species of Eretz Yisrael (grapes, figs, pomegranates, olives and dates), then the sequence of precedence is: olives, dates, grapes, figs and pomegranates.
4) If one is drinking wine and also eating fruits from among the seven special species, then according to the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), he first recites the Beracha over the wine before partaking of the fruit. This follows the position taken by Rabbenu Peretz (France, d. 1295). However, Maran (author of the Shulhan Aruch) in his Bet Yosef rejects this ruling, and does not bring it in Shulhan Aruch. Accordingly, Hacham Ovadia Yosef ruled that in such a case, one can choose either to first recite the Beracha over the wine or to first recite the Beracha over the fruit.
5) If one is eating foods requiring "Ha’etz" and foods requiring "Ha’adama," then, according to the Shulhan Aruch, there is no required sequence, and one can choose which food to eat first.
6) All Berachot precede "She’ha’kol," and so one recites a Beracha on all other foods or beverages before reciting a Beracha over a food or beverage requiring "She’ha’kol."
Summary: If one eats bread with other foods, he recites the Beracha over the bread first. If he eats "Mezonot" food and other foods, he first recites the Beracha over the "Mezonot" food. Fruits from the seven special species of Eretz Yisrael precede other fruits, and all foods precede foods requiring "She’ha’kol." If one is eating foods requiring "Ha’etz" and foods requiring "Ha’adama," he may eat either one first.