Long story short, here's my process through implementing a character animation for the main locomotion in Unity.
This includes a lot of iterating, and a lot of searching on how could I make it in a way that fits the game the most, and fits the resources I have.
The first picture showcases the animator, as i've layed out the layers. Do note that the Locomotion is on another animation layer.
The second picture is the first step I've made. It's as simple as it can be, but I was not too happy with it because it felt too rough.
The third picture is the second implementation, probably with the main changes. This version includes strafe and better direction handling. Do note that I'm forbidding the player from walking backwards because it makes no sense in my context.
The last picture was a small modification I've made after looking at the Unity standard third person controller, but I was not really convinced that it made a difference at all. So I just.. don't use it, I guess.
The last picture has an add-on for the static movements, such as turning in place and idle. Hurray for nested state-machines !
No body allowed!