I swear by the fridgesmart containers from tupperware - a bit expensive to start out with but well worth it in the end.
We are the same. I use a large container for my carrots, cucumber and celery sticks and then put into two smaller containers whatever other vegies I have purchased which is usually broccoli and cauliflower (I cut up into chunks before putting into container so so easy from a cooking perspective), mushies, pumpkin and capsicum. They keep the vegies fresh for so much longer. If I have strawberries I will also put them into one of these containers. I keep vegies all in one crisper and fruit in other.

On the fruit side I simply have a large plastic bowl that I put in my crisper filled with apples, pears and whatever other seasonal fruit we purchase. The fruit tends to get eaten pretty quickly in our household so I dont need to store it specially. I also put bananas in the fridge just because otherwise I find they ripen too quickly.

In my pantry I have one of the large tupperware vegetable storers where I put my sweet pot, potato and onions. It also does keep them longer too. As you can tell I am a tupperware fan.