I assume we can also go beyond peak human physiology right?

Yeah you can maybe at battles since in that you can sometimes break your limits, through pushing yourself at its limits or because the intensity of the battle

Then I would choose Absolute unarmed combat mastery.

Ah, I also forgot that when wielding any weapon you can basically achieve supernatural feats... Or just straight at break your limits when wielding weapons or objects..

Absolute Unarmed Combat, because in this case your body is your greatest weapon and your greatest shield. The other option relies on weapons to become powerful, what if you have nothing around you to use as a weapon? Anyway, the first option interests me more.

Absolute Unarmed Combat Mastery easily. My body is my weapon and I don't need an external object to help me. Like @Mr. Saggo Ramer said, what if there is no weapons around? Besides, you know Baki right? So you know how cool and epic unarmed combat is. Sword? Nah, I can use my fingers to cut. Hammer? My fist would be more than enough. You can also use other things, like for example, pressure points

You think a User of Absolute Weapon proficiency could utilize the air itself as a weapon? Anything could be a weapon theoretically.

You know what's a weapon? THESE HANDS!!

Unarmed combat and armed combat are one and the same. It just the application of the same stuff. You just have to exploit the concepts between them.

Let me show you