We have a cool room in our basement which works well for storing vegetables through the winter.

I store apples, potatoes, squash, onions, cabbage and sometimes root vegetable. I stored carrots until we got the greenhouse.

We grow our potatoes in the ground, not greenhouse. We dig them, hose them off and when they are pretty dry I put them in a storage shed laid out on a tarp for acouple of days to really dry well. I sort out the babies for seed and store them away, sort out any that got cut in the digging for eating right away, then store the rest in wood produce baskets. They last until spring in the cool room.

Onions I hang in a net bag, the rest goes into wood baskets.

You can pull carrots and store them straight up in a 5 gallon bucket with moist sand in it, and they will stay alive and sweet. Or some people use a wooden box, and lay them down more in layers with sand in between.

Check your produce occasionally to make sure no bruised produce got in an started to spoil.

A couple of years ago I got a dozen baskets 18" ones from Texas Basket.
[link to www.texasbasket.com]

We grow enought to store and share. We do not have a big setup like OP, but our small garden produces plenty to share with neighbors, store/can/freeze and for us to eat off of most of the year.