You can easily find the right gauge wire by storing it in a divided plastic envelope, like those used for office supplies.
Label each divider by gauge (10, 12, 14, etc.), and "file" your wire into the appropriate section.
If the wire arrives in a plastic bag from the vendor, I sometimes leave it in the bag when storing it.
But the envelope closes tightly enough that I often skip the extra bags altogether.
Too many plastic bags can get bulky and hard to manage.
I've never noticed any oxidation in my stored wire, so this simple method works well.