If I was going to use a fridge (hoping that it's your dedicated garden fridge) I'd wrap the dahlias in newspaper and write down the type/colour on the outside with a permanent marker felt tip pen (plus the date you wrapped them - just in case). About three sheets thick.

I'd do the same for the begonias - once they'd dried enough to gently brush off the old dirt and roots. Ancient toothbrushes can be good for doing that. Noting the colour and style of the begonia is critical if you want to plant up without going through the stage of potting up and waiting to see the first flowers before planting into a final site.

If you don't have zillions of tubers (you're a newbie, you said. You might still only have a 'few'...)you can leave them in their pots over the winter, old mix and all.

Those polystyrene shipping trays for grapes - the ones with the lids - can be very useful for storing your begonias and glads with protection, air circulation and some separation between the individuals.

For the Anemone coronaria I'd usually say - pot them up so they can be growing on for over winter. However, with your zone, perhaps just in a net bag in the fridge - cool, dry, 'airy' so you can plant up in spring.

With your Fairy Lilies - are they autumn or spring flowering? And, which sort, please?

The Peruvian daffodils - the fridge might be a bit cool for them. Once the leaves are off - store upside down in dry peat, in shade. (So a suitable closet could work.)

Why would you store bulbs in the refrigerator?

If you are storing bulbs, or putting them in a refrigerator to force, it is important to remember that ripening fruit puts off an ethylene gas that will kill flower buds in bulbs. So no apples, etc in there with those bulbs!

Based on my bad experience, I would like to point out another thing that every time when you open the fridge, the moisture in the nearby air quickly get condensed on the cold objects inside the fridge and causes the mold to grow, so wrap your bulbs/tubers/corms in a plastic bag or anything like that to avoid this...