The Japanese Anime I have watched as they aired that ended in the Summer 2018 broadcast season (From around the beginning of July 2018 to around the end of September 2018).
Shows are listed as their separate 'seasons' to conform with Japanese series formatting, see any attached notes.
(Before this season, I had not watched currently airing Anime since the 1990s, so this is a very short list.)
Best overall:
Mirai
Best animation:
Mirai
Best story:
Mirai
Best music:
Persona 5 The Animation
Most surprising:
Persona 5 The Animation