A few weeks ago we went to Costco and picked up about a zillion pounds of fresh produce. As soon as we got all the stuff up to the apartment we were like "Oh I guess we need to eat all this before it goes bad?". NOPE! I did some research and experimentation and below is what has worked so far. The key lesson I learned is that, as always, my mom was right: "one bad apple spoils the bunch" i.e. don't let your fresh stuff touch, because when one thing goes bad, it turns whatever it's touching bad.
Line bowls with paper towels and store tin he tomatoes in the bowls (I used our massive sized unused tupperware). Geometry was my first C in high school so I had a REAL hard time figuring out how to arrange these damn tomatoes without any of them touching.
When I worked in afterschool programs we would get massive amounts of bananas. All you have to do is unattach them from each other and put them in the fridge. They'll look brown (ew) on the outside after awhile but they're perfectly fine under the peel (really all the childhood lessons my mom taught me are coming back in the form of produce).
You can freeze any fruits that aren't super juicy (so blueberries, raspberries, etc). You CAN'T freeze watery things (apples, spinach, lettuce, etc). Also I had a roommate who used to eat frozen grapes. You can only freeze grapes if you want to eat them frozen for the rest of their existence. They don't thaw out too nicely.