This is the list of things that I am supposed to bring to (or have at) class.
Many of these items are ones that are also useful to any home bread baker, so I’m listing them here partly as a cross check.
What are the differences between equipment, ingredients, and supplies?
Equipment is used to make bread. It’s durable, that is, it is not used up in the process of making the bread.
Ingredients are used up to make bread and are significantly incorporated into the bread.
Supplies are also used up to make the bread, but are not significantly incorporated into the bread.
Much of the equipment is in some respects optional. If you had a good work surface, and didn’t mind getting your hands messy, you could get by with just a good work surface, a bench knife, and a wire cooling rack.
You can make decent bread that way, but you would not be able to be as precise (or tidy) as many people like.
The very leanest dough needs only flour, water, yeast and salt.
Often, when proofing the yeast, you add a little sugar to help the yeast get started.
If you are making an enriched dough, you might add some source of fat (butter, oil), and an egg. If you are making a sweet enriched dough, you might also add more sugar.
If you are trying for a tender sweet enriched dough, you might also add powered milk and potato flakes.
If you are making bread using whole-wheat or rye flour, you can make the dough more likely to rise well by adding vital wheat gluten (which you can buy from the local co-ops in their bulk food sections, usually in their coolers). You would use about a tablespoon per loaf of bread.