From my time in the Produce Shop

Back around the time that I was married (and that's 23 years almost), I worked in a mom-and-pop produce store near Portland, Oregon. The place was owned by Italians, especially a very proud owner named Frank, who did appearances on a local tv show from time to time with advice about produce. I learned a lot, but I had four passionately opinionated and not-always-in-agreement Italian bosses, which was quite an experience! I could be setting up the tomatoes, and each one would come by with a different way of doing it right. Kind of funny, looking back. It was a good experience, overall.
Which brings me to tomatoes...I bet you keep yours in your fridge, don't you? "Of course, where else would I keep them?" Actually, this is one of the more revolutionary things I learned there. Tomatoes keep better and firmer out on the counter; in the fridge they turn watery. Sure, they do spoil eventually in either place, but if you like firm tomatoes, keep them at room temperature.
Bananas can be kept in the fridge if you want them firmer longer. The peels will turn ugly, but you're not eating the peel anyway! Apples and oranges should be refrigerated, but I like mine on the counter, because we forget they exist, in the fridge.
Onions and potatoes should be kept at room temperature in the dark, but not together because one makes the other sprout, I'm not sure which one. I keep them both in my pantry, but not next to each other. If potatoes see too much light, they turn green-tinged, and the greenness can cause stomach aches. If you just peel it off, it's fine underneath though.
Cantaloupe and other melons should give slightly at the blossom end. Honeydew melon should be waxy-feeling on the outside. Watermelon should sound rather hollow. (I bought one one time, though, because it sounded so hollow--and it was! The thing had rotted inside. Don't go for TOO hollow!)
Broccoli is best if it's kind of stiff, not wiggly, and if it has a kind of purple hue on its buds; the buds shouldn't be open and there should be no yellowness anywhere. It keeps best on ice. If they don't have it cold, don't buy it.
That's the most significant and memorable stuff I learned in the produce shop. Hope it's useful to you!