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.
EDIT: It's very difficult to determine the number of currently obtainable outfits as most trustworthy sources only wrote outfit guides when the game was released and didn't update them when DLC was released (most of which included new outfits).
Based on this video which seems to be complete, there were 13 new outfit and hat combinations as well as the 8-bit Mario Cap added as DLC. This brings the total to 55 hats and 55 outfits.
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.