Not sure about Katanagatari, seems a little childish and hearing the characters talk about "I use xxx-style, well you will never defeat the xyx-style" really puts me off (that is not good story telling!!)
It isn't childish, it is tagged seinen for a reason, also it is the same writer as the one of (bake)monogatari series, so if you liked that show I'm pretty sure you will like katanagatari too

What you are looking for is
Holyland, I doubt you will be able to find any better suggestion than this,
since it fits your request pretty much perfectly. Scratch that, it is exactly what you are requesting. Even if you don't normally read manga, you will wanna do it for this one. The mangaka Mori Kouji have been studying a lot of street fight, material art, and participated in street fight to make it as realistic as possible.
Slightly off-topic
What kind of training/material art are you doing?