Drill holes and run them through the joists. Also, paint the ceiling if you want to hide it all.

There are no joists. Running the wires I can do neatly. It's mostly the connections. I'm thinking about getting a bunch of the lever splice connectors

What kind of fixtures do you have that show the connection?

They are led light that have plug in pigtails.

Code does not allow connections to hang in the air; they must be enclosed in a junction box.

The easiest way to have a neat arrangement is to use Wiremold products, which has boxes for junctions and switches, and flat conduit that can be run along the walls.

make sure to stay 2+" from joist edges

Conduit done well can give a really clean look. More expensive, and more time consuming to install, but done properly will be up to code and look clean.

This will be about the spot in my house I can actually wire everything from scratch. The lights now are shitty fluorescent lights with wires running everywhere.

NEC code, if I recall correctly, is 1.5 inches before it needs to be covered by a nail plate.

Like others have mentioned, you cannot leave wiring exposed. It’s a fire hazard and a safety risk for everyone in your house. If you cannot conceal the wiring behind a wall, use a conduit like EMC or Wiremold.

This isnt NEC, its structural

Plastic nail-on boxes for all permanent house wiring. All connections inside the boxes. WAGO connectors are fine. Run your fixture pigtails out of the boxes.

The wiring for the lights would be like 9 feet off the ground. When I had the house inspected he did t say anything about having to redo the crappy wiring that was already there

Can I just run the cable and then have a junction box at each light? And not use conduit

It depends on where you live. I would check local codes first. One town I lived in required conduit and another town I lived in required BX cable or Conduit but not Romex cable. Don't ask me why.