I'm not up on all the associations, but you don't want to store some fruits and vegetables together. Ethylene gas is a ripening agent and some items put off more than others.
Bananas are an example of its effect. They are brought in green and then put in a "gas chamber", given a shot of gas and then shipped. The strength of the process can be seen in bananas. You see them in the store where some are still pretty green, but it doesn't take long before they ripen, which by the way is when they turn black.
If you're going to have fruits and vegetable for any periods of time it would probably be a good idea to Google up the pairings to avoid.
It's also generally a good idea to store vegetables as they are displayed in the grocery store, not a stand. If they are under refrigeration, keep them that way, if not don't put them in the fridge. There are exceptions, tomatoes comes to mind, they don't seem to be bothered by refrigeration and it does extend them some.
