How should I organize my fruits for storage?
Anything that outgasses ethylene should be kept away from other items (both fruits and vegetables), in a well-ventelated area, if possible.

Apples and bananas are the two most common culprits, but the list is much longer.  Subzero has a list of etylene producers and ethylene sensitive items, which I'm reproducing below in case of link rot:

Ethylene producing foods


apples 
apricots 
avocados 
ripening bananas 
cantaloupe 
cherimoyas 
figs 
honeydew 
kiwifruit 
mamey sapote 
mangoes 
mangosteen 
nectarines 
papayas 
passion fruit 
peaches 
pears 
persimmons 
plantains 
plums 
prunes 
quince 
tomatoes 


Ethylene sensitive foods


unripe bananas 
green beans 
Belgian endive 
broccoli 
Brussels sprouts 
cabbage 
carrots 
cauliflower 
chard 
cucumbers 
eggplant 
leafy greens 
lettuce 
okra 
parsley 
peas 
peppers 
spinach 
squash 
sweet potatoes 
watercress 
watermelon