I've never done classes with a pup, I've always trained them myself, so sorry, can't give you any recommendations there.
I much prefer wire crates. I like the sturdiness of them, the ventilation and how easy they are to clean.
Always use a harness for training & walking. I know some on here use breakaway collars for ID tags for their pups, but not to attach a leash & walk them.
Congratulations on your new puppy! How exciting
