you really must have the Audubon Field Guide to North American Mushrooms.
It has very good information, including whether the mushrooms are edible, good or choice, or poisonous or fatal. (Study those fatal ones until you know them in your sleep, and just stay away from any mushroom that could be mistaken for them. Poisonous usually just do not sit well and can make you uncomfortable but will not kill you---not that you shouldn't avoid them.)
It tells you how to do spore prints, which are important to really learning some of the mushrooms. It tells you how to cook the different kinds. It lists any look-alikes, so that if you "think" you have found a certain species, you can determine if that is what you have. So for the most part, this is a good handy reference.
For a winter project, read up on things like how to do spore prints. Also familiarize yourself with the different types of mushrooms, like gilled and boletes, as well as whether the gills run down the stem or not. Notice that some mushrooms have rings on the stem. And some mushrooms are irregular in shape. Once you are aware of all the details you can look at to determine the species that you have found, it will be much easier to identify them in the field.
When you go out for mushrooms, bring paper sacks or a basket, or both. Baskets are nice to keep them protected, and the sacks can keep different mushrooms separated. Never put them in plastic bags.
See if there are any mushroom clubs around you. I find that they are very helpful to beginners and often they have foraging walks and identification talks.