What's the best way to create a custom character with custom animations?

A great example of my question is this:

What’s the best way to achieve creating animations for a custom character? Should I use Roblox’s default animation tool or should I use sine/cosine functions to manually move parts? I want something similar to Robot 64.

I personally would use built in animations, but it is honestly up to you. You need a rig, once you have that either use built in animations and play around with Weight or use lerping and CFrames. Really depends on what you are good at.