I know generally speaking, when prioritizing brachos, if you have food and drink, the food goes first; also, shehakols tend to rank low.
But what if you're really, really thirsty (e.g. breaking a fast), and you have a cup of water and a cookie. Which bracha do you make first?
The issue isn't so much ranking as it is intent. If you say shehakol while having the intent of eating the cookie, you are yotzei(albeit b'diavad) on the cookie as well(see the second mishna in Keitzad mevarkhin, 6th perek of Berakhot for an in depth analysis).
Going from the minhag in both Yeshivat Beit El and Yeshivat Nahar Shalom when they break their fasts after tikkunim, the drinks are brought out first, everyone takes and blesses, and then the food is brought out. If it is not "before you" you still need to make a berakha. Some poskim rule this way even in the midst of a seuda(such as the Ben Ish Hai, will find location soon).
Ultimately I think what would be best would be to pick up your drink, make your berakha on that, and then pick up your cookie.
Background- Shulchan Aruch O.C. 211
Mechaber a: If the brachos are different, there is no kadima (211:1)
Mechaber b: If the brachos are different, you go by what is generally you favorite (211:1)
Rambam: If the brachos are different, you go by what you want now (211:2)
Mechaber: The above is only true when dealing with brachos of similar specificity, but when one bracha is more specific, the more specific bracha is first. (211:3)
Halacha lemaase: Mezonos is more specific than shehakol and would come first under all circumstances. See the mefarshim in more detail for haetz vs haadama.
[There is a Biur Halacha which cites the Eliya Rabba in the name of the Shela a general practice of people who make a bracha on schnapps before other brachos with more specificity (e.g. haetz). He suggests to their benefit that they really only want the shnapps at first and their desire for other foods is only after the drink. The BH recommends eating the haetz first, nevertheless, since eating after may render the food tafel to the schnapps]
I was learning something related in the Sefer Vezos Haberacha (וזאת הברכה) and came across this exact case!
He writes (in Perek 13, in the context of discussing cases that are exceptions to general rules of "ordering of brachos") [loose translation by me]:
וכן אדם שבא לאכול סעודה, ורוצה להקדים ולשתות לפני הסעודה, מפני שהוא צמא, רשאי לעשות כך אף שמברך ׳שהכל׳ לפני ברכה אחרת יותר חשובה, כי כך הוא סדר הדברים למי שצמא (פה״ל פ״ה הע׳ ד׳
And also someone who wishes to eat a meal, but first wants to drink because he is thirsty, is allowed to do so even though he is saying Shehakol before any other beracha which may be more chashuv - because this is the normal procedure for someone who is thirsty.
So, in short, you are allowed to make a bracha on the cup of water first.
His source appears to be the Sefer פתחי הלכה by Rabbi B. Forst (who is also of The Laws of B'rachos fame). However, I was unable to find this exact case in either of his Seforim. He does however discuss (which is also brought in the Halachos of Brochos by Rabbi Bodner) the general exception to the ordering of brachos in cases where there is a specific reason for changing the order (the example given, if I recall correctly, is having the appetizer before the main meal, where normal brachos rules would dictate otherwise).
I also want to point out that this last novelty is said even in a case where both foods are directly before him. For if not, the rules would allow him to say the bracha on that which is before him, and not require him to go and retrieve the other item.
