If you create a new set of armor in the Creation Kit, how would you make it go into a specific tab in the blacksmith's forge. For example, Iron, Steel, Dragon, etc.? And most importantly, how would you create a new tab?

It's a keyword on the item (and I think on the crafting station where it's made). All items with the common keyword are grouped.

Armor gets keywords for construction and sale - i.e which vendors sell it. There are material keywords for matching sets also. Take a look at the Skyforge and what you can make there for an example.

You can add your own keywords, for example if you want the armor to be constructed only at a special forge, or constitute a new matched set.