I don’t think (3) is correct. Or at least, it’s redundant, As far as I know, Green Flame Blade and Booming Blade are the only spells that allow you to make a melee Attack with a weapon as part of the spell effect. As well, there are a couple of spells that create a melee weapon with which you can make Attacks, and those attacks are appropriately melee weapon attacks.
3 is necessary because otherwise the combination of 1 (with a weapon) and 2 (without a weapon) would include every attack, including spells.