For the oaks and the hickories (and anything else with larger seeds), i like to stratify them in lightly moistened sphagnum moss, which really works well for deterring mold. Sphagnum is too coarse for smaller seeds though, so for them I use a lightly moistened paper towel in a ziploc.
Your fridge should be kept as close as possible to just a few degrees above freezing (34 is perfect). Put several thermometers in your fridge to find out where the coldest/warmest places are. Often the place right next to where the cold comes into the fridge from the freezer unit will be too cold and you will freeze any seeds that you put there. Additionally, sometimes the very bottom of the fridge will be a couple degrees warmer than the top of the fridge, as the compressor in the bottom gives off heat.
If seeds get moldy, you can give them a misting of hydrogen peroxide and put them in a new paper towel. I usually have to change out the paper towels ever 4 to 6 weeks, but some seeds get moldy a lot faster than others, some don't really get moldy at all. A little mold doesn't hurt them, and you can usually tell seeds that have gone bad because they go soft and squishy. A good pair of tweezers really helps for working with seeds in paper towels.
As for time required for different species, I usually go by the listing on sheffields.com. Often seeds will start germinating in the fridge, so you will need to check them every couple weeks at first and then at least once per week later in the spring, to pluck out the germinating seeds and place them into your growing medium.