Well, we are extreme opposites here. Rather than trying to keep fruits/vegies happy for long periods, I shop on a nearly daily basis. Produce can’t go bad if you use it the day it is purchased.
Well, different people will have differing time management strategies and priorities.
Mine keep for almost a month - taken out of the bag, in a box lined with newspaper in our pantry closet which is away from light & heat.
I bought these containers. See the holes around the bottom? Taters, onions and garlic all stay fresh a long time.
What you can do, with a small apartment and not much space, is buy one of those triplicate hanging baskets, and dangle it from the ceiling. You can put potatoes and onions in these, just make sure it’s secure so the whole thing doesn’t come crashing down on your head one day.
Is that the hard-won voice of experience? 
From scanning the literature on commercial potato storage it seems to me that you want to remove carbon dioxide and prevent formation of sugar. So a cool ventilated place outside the refrigerator, perhaps.
Bah - I rarely deep-fry my potatoes, so in the fridge they will stay.
(First thing that came to mind.)
I was curious myself and did an experiment once. I took six potatoes and put half in brown paper bags, and half in plastic bags. Then I put one of each in the cupboard, one of each on the counter, and one of each in the fridge. The one in the brown bag in the fridge looked good-as-new 3 weeks later and the rest had all sprouted or gone mushy. Unfortunately a bag of potatoes takes up too much room in my fridge. I need that space for rotting leftovers!
That is a lot of maybes about what appears to be a slightly increased risk that is apparently there anyway every time we eat a french fry. I cannot say I am terrified. I live in Southern California, and, much of the year, nowhere is very cool. Also, I believe, as potatoes start to sprout the concentration of natural toxins in them increases. So far, I am not persuaded that I am silly to keep them in the fridge, especially as I mostly boil them. (I occasionally roast. For fries I use the frozen ones.)
The onions problem is probably a myth, even though it’s been an Idaho potato growers website, as well as Martha Stewart’s and hundreds of others.
I asked about it in GQ one time, and the only counter-evidence I had was from the U of Minn Extension Service saying it was a myth. A whole lot of dopers wrote that their families had stored onions with potatoes with no problems.
Heh. Less than three hours ago I threaded wire through a triple decker basket’s chain to keep it from dumping potatoes. We had had one for years that finally wouldn’t stay together, and the wife went out a bought a new silver one a few days back. It collapsed under a load of potatoes and onions the first day it went up.
So, I threaded picture hanging wire through the chain tonite, to take the load off the cheap ass chain. Doesn’t look awful.
I looked up the acrylamide thing (I almost typed “thalidomide” - it’s waaaay too early for me to be up), and the general consensus is there is indeed acrylamide in some foods, they basically know how much, but they don’t know how much is too much. Studies are still in progress.