How do I pick which line weight to use without overdoing it?

The rule of thumb your senior guy gave you is basicly it. Visible edges get the thickest line, section cut lines can match that or go slightly heavier, and everything else, hatch, dimensions, extension lines, centerlines, hidden lines, goes thin. Hidden lines sometimes sit in a middle weight if you want them to stand out a bit, but if your sheets look flat right now the problem is almost certainly that everything is one thickness, so just split it into thick and thin and you'll see an instant difference. A common way to think about it is visible edges roughly twice the weight of the thin stuff.

Yeah that thick vs thin split is exactly what fixed my sheets back when I started. One thing I'd add on the colour question, colours are just for your screen, most of it prints black anyway, so don't stress there. I got in the habit of printing one test sheet on paper before sending anything to the plotter, and you can spot a flat drawing straight away that way. Also set the line weights once in your document template and save it, then every new drawing starts right and you never think about it again.

This might sound dumb but when I zoom right in on the screen all my lines still look the same thickness no matter what. Is that just a screen thing and it only shows up properly once it's printed? I keep changing stuff and staring at the monitor and can't tell if I've done anything at all. Also the dashed lines, the ones showing edges you can't see, are those what people mean by hidden or is that something else entirely?

To answer the question in that last post, yeah the dashed lines are the hidden ones. Dashes mean the edge is there but you can't see it from that view, like a hole on the far side of the part. Phantom lines and centerlines look diffrent again, they use long and short dashes mixed.

On the screen thing, I stopped trusting my monitor ages ago. I do a quick print preview or print a cheap copy on the office laser and judge from that. Paper never lies.

And to the template question, set it up once and save it. I copy the same template file into every new job so all my sheets come out identical, zero tweaking per drawing.

One thing that tripped me up for ages in SolidWorks was tangent edges, the ones where a rounded face meets a flat one. They show up solid by default and they make your thick outlines look even heavier and muddier than they should. You can leave them on but make them display thinner, or turn them off entirely on some drawings, and honestly it depends on how much detail the shop needs. I woud also say do the setup once in your document template and save it, because if you tweak weights drawing by drawing you will end up with sheets that don't match each other, which is its own kind of flat.