Best case for note 3

I got the Otter Box Defender series and i'm happy with it. Another nice thing about it besides the built in screen protector, Is that the clip attachment also acts as a dock or phone stand
 
Be careful when buying non Samsung S-view cases since they have chip in them to operate the s-view functions and the cheap imitators don't work with the new Andriod OS. Just go ahead and spend the money on an official Samsung case or you will be sorry.
 
I use the Samsung Flip Case. I always used Otter Box cases for my phones prior to this, but I find the Defender a bit too bulky for my taste.
 
I don't know about folio cases (I've always carried my phones in my pocket if they were small enough, or on my belt), but I've been using the iBlason holster case ($12.99 now at Amazon) for over 6 months, and the phone feels funny without it. It's TPU, so it takes up a lot of the shock if you drop the phone, it's not slippery, so it's difficult to drop the phone unless you're careless, and the case protrudes about 1/16" past the screen, so even if you do drop it face down, it's the case that takes the shock. It also has a nice little kickstand if you want to prop the phone up in landscape mode to watch TV or a movie.

The TPU part is black on all of them, but the colored part can be taken off, so it can probably be cleaned pretty vigorously.