AA or ASW is the "normal way" to level fastest.

Although some may say that rentals and powerleveling on different ships may be faster. 

ASW worked up the mogami, then i messed with AA'ing planes with some ASW weapons as well. Myoko is all AA with a few binds of HE Light. Wait for a unspecting SS to surface and wham

It's 200%.  You could twiddle your thumb and make it to Kongo by the end of the day.  On a serious note, AA usually ends up being the fastest but right now anything works.  Don't go the TW route though if you are going to be playing the BB line.  It has few support slots not to mention part of the crew would be wasted on torpers.