It really depends on what you're keeping in the fridge.
In my Navy days, we basically had areas for different type of products, which were organized differently.
What we used to do was more or less this:
- Vegetables: This is more or less per vegetable, but worked for us. For instance the carton of tomatoes or cucumbers next in line was on a middle shelf, next to all the other vegetables next in line for their type. The other cartons were stored right at the bottom of the rack, basically on the floor. Once a carton was finished a new one was moved up in its place.
- Peeled vegetables: We occasionally peeled enough potatoes (or carrots, or onions) for 2-3 days. In this case, the potatoes were stored in a kind of bin with water. Unpeeled potatoes were in sacks in the back of the fridge. Once the peeled bin was empty, we'd change the water and peel more potatoes.
- Meat: Most meat was in the freezer for reasons which are obvious once you're carrying supplies for more than a few days. However, every afternoon the next day's meat was moved into the fridge for defrosting. It had it's own cabinet in the fridge on one side.
- Dairy: Dairy products usually came in trays for us, and there were never too many of them as we were a 100 person galley. These are generally light enough so that when a new shipment arrives, you can just lift the old things and place the new ones under them. At worst, you take the old stuff out, put the new in, and then put the old back in on top.
- Prepared dishes: Sometimes we'd make a coleslaw or something in the morning to serve for lunch. Obviously, it needs to be refrigerated during the wait. These things had their own shelf, and were put there until needed. We'd only ever have those for the next meal, though, so not much of a queueing issue.
- Special items: Anything that was particularly special (rare or expensive) was kept in a 3foot cubed locked cabinet in the fridge, where prying hands couldn't reach. Hopefully, that's not a concern for you.
That's it. The only other adivce I have is to use big (gallon, half-gallon) modular boxes that stack well, if you need to keep a lot of prepared things.