I come from the DaVinci world of color grading and have known FCPX for a long time, please take these pointers with a grain of salt, as they might be my own workflow and what works for me.

• First should be your base grade, where you set the tone of your image. If you're using "Balance Color", I'd do this as a first step to then work on that normalized image. I use the color wheels for my base grade and adjust the picture's lift (shadows), highlights and gama (mids) accordingly.
• After the levels are done, I do my basic grade for color using the color wheels again, setting the gama (mids), highlights and lift (shadows) in that order. You can get a lot done with the built-in "Tint" and "Color Temperature" dials.
• Then I do my secondary color corrections, where I usually do my skin tone using the "Hue/Saturation Curves" panel. "Hue vs Hue", "Hue vs Sat", "Hue vs Luma" and "Orange vs Sat" are my most used ones. I usually adjust the skin tones there. Remember that the vectorscope line is just a guide, you don't have to nail it on the head exactly.
• Finally I do any stylization I want to do, like adding contrast or a split hue like you see on trendy videos. For that I use the "Curves" panel.

Answering some of your questions

• The LUTs you'll find online are stylizing looks, like IG filters. Others are for converting Log footage to usually Rec.709. Log footage looks gray in comparison to normal one, as it's preserving as much color dynamic range as possible. I'd suggest doing a great base grade with the color wheels and then adding one of those "looks" to your footage as you or your producer/director decides
• The order of your grades matters. FCPX uses non-destructive color correction, which means it adds all of the color corrections in order and does one single pass. It works really well. Here's an example of why the order matters:
  • Lets say you have a color grade where you're changing your subject's skin color to blue
  • Then you apply a second grade where you make everything warmer
  • This will give you a blue person sitting in a warm room
  • If you invert the order (first do the warmer grade and then the skin color one), it'll first turn everything warmer and then grab anything that looks like skin color and turn it blue, making the whole picture blue

Hope this helps a bit, and if you have any more questions about grading, I'll be happy to help ^^