Do you have a large plastic container? Something like this:
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Use a non-permanent marker on the outside to mark the initial volume.
A small diameter will make it easier to monitor the volume.
The best recommendation I have seen is plain plastic wrap. If you have an oil mister, mist the wrap before using it. If you don't, pour oil into a bowl, enough to form a puddle, and toss your ball of dough in the oil. Then transfer your dough to the rising container (if you use the same bowl you used for oiling, take the dough out, pour out the superfluous oil, return the dough into the bowl). In the best case, the bowl will be deep enough for the dough to rise without the middle touching the wrap, but if it rises more (even with the dough pressing against the wrap), dough with enough gluten development will peel off the oiled wrap with minimal losses, even if it is wet.
The wrap will keep your dough surface moist in both the fridge and outside. It doesn't allow breathing, but this shouldn't be a concern in most cases. If you overyeast the dough, the collection of fermentation byproducts in the bowl will probably make for worse taste than if they are allowed to dissipate, but the correct solution for this problem is to not produce them in the first place. With your "very long times", this is probably not a problem in your case.
You can also use this method for the secondary fermentation. But in the final proofing stage, you have to make sure that your dough never rises enough to touch the wrap, or else the loaf will deform while you are removing the wrap. Also, if you are proofing in banettons, don't oil them, use flour combinations to prevent sticking.
If you are out of plastic wrap, substituting alu wrap is a bad idea, because yeast is very sensitive to metallic ions. Today's non-reactive metal utensils are safe enough for use with yeast dough, but untreated aluminium can be problematic. Try baking paper instead (you may have to tape it to the outer bowl walls).
Best Answer
The goal is to keep the surface of the bread from drying out.
A wet towel works fine but plastic wrap is cheaper and easier than constantly cleaning wet towels.
I have used both methods and haven't noticed a difference in the bread produced. In very dry climates, when I made bread with multiple rises I sometimes had to redampen the towel which was an added inconvenience.
Lately I have been proofing large batches of bread in a large stock pot and just use the lid of the pot as the only cover.