As the title says, I just want to know the total number achievable, and don't care about the names. Also, are there any outfits you can only get with amiibo?
You can find the list of all outfits from various sources such as this one from IGN. There are 43 distinct costume sets though 3 of them only have one piece rather than both. The skeleton suit and boxer shorts only have body pieces while the invisibility cap is only a hat.
This brings the total to 41 hats and 42 body outfits. There are no outfit pieces that you can only unlock via Amiibo, though they can be used to unlock some of the more expensive pieces such as Wedding Peach and Wedding Bowser.
As of writing, including DLC, there are 49 hats and 50 outfits. However, data miners have confirmed several more outfits and hats to come, bringing the total to 54 hats and 54 outfits.
As of writing, the missing outfits are Harriet, Spewart, Zombie, and Santa, while the missing hats are the same four, plus 8-bit.
They keep adding more. I believe there are currently 48 hats and 49 outfits.