As a collector who has completed the type set, the half cent to the gold, as very often defined, I think you might find that you will be "collectors' fatigue" with all of the types as they are now defined. My least favorite types are the 1873-4 With Arrows coins. They are expensive, and once you hit a certain point, it's like filling holes.
As I said the old blue Whitman Small coins types set that I began with (back in 1972) did have holes for all 8 of the types I mentioned.
I include six for my type set. Same as your list. I can see a good argument for 8, but if "designs" are what drives it, 6 makes the most sense to me. Five just seems a bit lacking, looking at you Redbook. Here are my six specific coins for the Types: