hmm, no science behind it, but i have pretty good luck with our new fridge. i can tell you that our fruit in particular lasts A LOT longer in our new fridge than it did in the old one. we had the original 'builders special' low end GE that was put in when the house was built 15ish years ago up until last year. when we upgraded to a new maytag french door (mid range stand alone type fridge, not a built in) last year, all of the sudden, our produce, milk and other dairy/cheese, etc. started lasting a lot longer. it does have a little humidity slider for each of the two produce drawers for fruit vs.veggies, but i have no idea what the fridge does differently for the two settings. we've found we get the best performance from it when the fridge is set at 37 degrees for this particular model (but it has a separate little vent to chill the milk compartment down lower - prolly 35ish?)
as far as what goes where, my general rule is to start with whatever the grocery store would do with it. so things like bananas stay out until *just* ripe (little to no green left, but has not darkend to the deeper yellow yet). then i put them in the fridge. they do brown on the peels, but the fruit inside stays firm and fresh for an extra 4 or 5 days. all of my farmers market fruit like plums, peaches, nectarines, mangos, avocados and apricots are the same. i leave them out until when they are *just* ripe (the tiniest bit of softness/give) and then put them in the fridge if we haven't gotten to them yet. grapes, cherries and berries that would be refrigerated at the store go straight into the fridge at home. i tend to wash as i use. i also try to rotate thru the berries/grapes i have on hand so i can cull any trouble makers and use the most ripe first. if i've picked multiple berries for the week, i start with the most mold prone first (generally use raspberries first, blackberries, strawberries, blueberries and then cherries).
root veggies that aren't peeled stay out. i don't buy in the huge bags tho, so i generally have no problem using before they start to sprout.
any veggies that would be in the chiller section of the grocery go straight into the veggie drawer, even if they come from the farmer's market, unwashed, unpeeled. but i tend to buy and use within the week, so maybe that's why i'm not having an issue?
as far as your cuc's go, any chance you're buying them ripe and ready to eat? maybe you can ask your produce guy/gal to help you pick a couple, one that's ready to eat right away, and one that will last you a few more days before it's ready to go? i also found a great little book at williams sonoma that i flip thru whenever i'm in their store about how to pick out each kind of fruit and veggie. i've picked up some good tips from it as well over the years.