There are many levels of refrigeration you may encounter...
1) No Refrigeration: Most FNB groups start out this
way. At this point produce must be obtained about a day or two (at most)
before it is used, which is okay if you do one meal a week.
When you pick up food to use for that day, check all the boxes in the refrigerator and outside the fridge. You will want to take veggies that work together, and leave ones that don't fit in, or that you don't have time to process.
For example, say you need a box of bell peppers and there are five or six boxes of them. One box is moldy. If you have time and there is room, dump it in the compost. One box has some dead peppers, but a lot of good ones. Take that box. Leave the other better boxes for use later in the week.
Use this same process for all fruits & veggies. Try to build your meal around what needs to be used right now. Greens and berries deteriorate especially quickly and won't wait. If you have the time and if there's room in the fridge, put boxes of produce that are okay but on the edge in the fridge for the next day.
Fragile produce such as greens, berries, grapes, bartlett pears and broccoli need to go in the fridge. Most root veggies (except yams, sweet potatoes and carrots), winter squash, melons, apples and lemons are okay out of the fridge if there is no room. Summer squash, peppers, eggplant, cucumbers, green beans and tomatoes are okay outside for a while if they need to be.
If you have picked up produce from the market and are bringing it for storage, plan to spend some time sorting and rearranging. Don't stack a wall o' boxes in front of a stack of older unsorted produce and leave, because then someone will have to move all those boxes to sort food. Are there six flats of moldy strawberries in the fridge? Take them out and dump them in the compost, putting all the plastic baskets, plastic bags, metal twist-ties, etc. in the garbage or recycling, and the boxes in the recycling area or trash. Quickly check out the produce. Put the oldest but still-usable produce in front or in the fridge. Look through this stuff to remove bad items that could affect the other produce. Compost boxes that aren't worth sorting. Put hardy new produce in back of, or below, the older, usable produce. While picking up the produce, do not accept items you know you won't use, for example, artichokes, coconuts, or 15 boxes of just about anything. Thank them but explain you can't use it. If you are worried that they might stop giving you food if you don't take it all, evaluate whether you need it or not. Is most of the food moldy, or just some of it? Be tactful.