Keeping your fridge organised seems to be one of the things people wish they could do better, or just do at all. For us, I use to start organising our fridge the day shopping arrived and then as things were returned to the fridge, they slowly hour by hour and day by day become cluttered, messy and then I'd lost where I had put the butter again.
I am now trying this approach and so far it seems to be working. It's been a couple of months and I'm happy to continue taking an extra 30 minutes after my shopping day to save hours through the week.
When I get the vegetables out of the shopping bag, I am immediately washing them and cutting them into cooking size and then popping into a big 7litre container. 3 of these fit perfectly along the bottom shelf of our fridge. I separate different things into these containers from vegetables, fruit, yoghurt's, and leftovers. I do leave certain vegetables whole as we all love carrots, just eating them raw and whole. We go through a bag each week just snacking on carrots, so I cut some and leave a lot whole. I also like to keep Kale in a bunch as I make Kale chips.
I now use the crisper for fruit. As we live in Queensland, our fruit doesn't seem to last long being out on the bench, so we put it in the fridge, specifically the crisper. This way, older children can easily grab out fruit anytime they want- be my guest kids! :-)
Doing this not only gives me more time during the week with my family and less stress at dinner time but it also means I use all of our vegetables up and I don't have waste anymore. These containers keep them fresh. You can also pop a piece of paper towel along the bottom to soak up excess moisture which will prolong the life of the vegetables too.
As I have small children at home with me, when I am about to do all this washing and chopping of vegetables I set up a game for the kids, something that hasn't been out already. Try keep a few things packed away so when you need to distract the kids for a bit, you have something "new" as a novelty. Or if it's been a busy day and they have been out, I will pop on a movie or play school. Anything to give me half an hour where I can get this done as it then saves me hours during the week, which means more time with the kids.