Most teams get groceries for the week and cook.Cereal and fruit for breakfast, then we can eat out at an ethnic food fave including Mexican, Indian, Malaysian and African for about $10 a person. Packed lunches are easy too. Dinner could include spaghetti, ordering pizza, catering from Chickfila or other home cooked recipes.

Pick someone to take the lead.
It will make life much, much, much easier if a single person acts as the go-to for everyone. This lovely individual will compile menus, devise lists, collect money, and possibly do the shopping, but WON’T prepare the actual meals. Foodies are always bizarrely up for this kind of challenge, but if no one wants the responsibility, promise a volunteer they won’t have to do dishes the entire mission trip.
Check allergies and dietary restrictions.
You obviously can’t cater to everyone, but you can make sure to avoid peanut products. Keeping a running e-mail thread is an easy way to do this, and a great method of keeping tabs on planning in general.

Find out what your vacation destination provides.
North Peachtree BC and First Baptist Doraville have onsite kitchens, cleaning products, toilet paper, coffee, salt, pepper, sugar, and other basic staples already there. A quick call to the church can help nail it down.

If you can swing it, bring a few food items with you.This makes sense for expensive products everyone might use (olive oil, coffee, etc.) instead of condiments purchased cheaply (mustard, ketchup, etc.).

Get an approximate headcount, then multiply it by the number of days in your vacation. 
The result is the number of breakfasts, lunches, dinners, snacks, and desserts needed for the duration of your stay. Your final drink number is all those added together. In other words:

13 people x 3 days = 39

39 breakfasts
39 lunches
39 dinners
39 snacks
39 desserts
195 drinks (1 drink per meal, snack, & dessert)

Add up the final total and divide by the number of people paying for food.
For this trip, all our meals added up to about $467. Divided by 13 people, that’s $35.92 each. We added another $4.08 to each create a nice even $40, and to account for any possible overage.

Go shopping.
You can take care of dry and frozen goods months ahead of time, provided you have storage space. Fresh foods should be bought much closer to the start of the mission trip.

Eat.
No explanation necessary.