Could someone give me tips on color grading this short clip?

I took some sample footage here (it's shaky, and slightly overexposed, but you can see the colors): https://youtu.be/yCBqjLRLPKQ

I shot it in C-Log (or that fake C-Log that you can tweak the Canon T3i to do half-assed).

I was having a tough time learning color grading, so I took this sample footage to practice with. I was wondering if someone could help me out with what I need to do to improve it. While I know that there is a lot of subjectivity to color grading, I thought there might be some basics that you can apply to most every situation.

I've watched several youtube videos on how to do it, but I only found one that seemed helpful. The main thing that they pointed out using your lumetri scopes for was:

• Anything in your shot that SHOULD be true black should be in the 0%-5% range on the Parade (RGB) lumetri meter using the blacks slider.
• Anything that should be almost 100% white in your shot should be in the 95%-100% range using the whites slider.

That seemed like good advice, and I know there could be instances where you do not follow this, but I'm not sure when.

So my questions are:

1. What would you do to improve this and why? The why is pretty important. Whenever I'm watching youtube videos, people will say, "ok, bring up the shadows", but they don't explain why they want to bring up the shadows.
2. I know this is 80% art and 20% science, but is there a more scientific method to color grade that I can use as a crutch while learning the art?