Let me add a little here, if you don't mind, Sub...
Okay, these are simply my experiences, but I figured maybe I could add a little from a traditional approach. It's been a few years since I was last employeed at an art store, but paper, pens, and pencils were my areas to cover because those were my things. As for my "street cred", I've had a few things published over the years, such as my "Home Made" strips in the early issues of "AG: Super Erotic Anthology Comic" from Icarus, a spot illo in the back of "Taxman" from Comics Conspiracy, and co-inks on its follow-up, "The Exec". As an example, from "The Exec", the blue line that follows is how I received one of the pages from my co-inker, and what follows that is when I'd finished it:
(We made non-repro blue line copies of the original pencils because the paper the penciler used just was not working well for inks, and to preserve the original pencils as much as possible)
I'm a believer that line art should be able to stand on its own, without the aid of colors, tone, or grayscale. Use the others to help add an extra layer to the art, but not as a crutch.
First let me mention line weight. Line weight is the variation in thickness of a specific line. The weight of a line can vary in a single stroke using a brush or a quill by the pressure applied, producing a thickness that goes from thin to thick or vice-versa. A deadweight line is a line that offers no variation in thickness.
Now, that aside, there are a few different schools of thought when it comes to inking. There's the approach you mention, where you work from thinner lines in the background to thicker lines in the foreground to make the layers of the art "pop". That way you can differentiate between the details, and know what the important aspects of the image are. You can combine this approach with other approaches, or you can use a deadweight line. A lot of people who use this thin-to-thick method seem to rely on layering deadweight lines.
Another relies on line weights. The standard line weight approach involves setting a light source and using thinner lines in the areas that would be more affected by said light source, gradually getting heavier, with the thickest lines being in the areas that would be furthest away from that light source.
Usually you want to get a good balance of white and black. It's like you turned up the contrast on your TV or monitor. Without tone, color, or grays, this better balances the page. The phrase, "when in doubt, black it out" can do you well, but really, like most things, when to really do that to get the best effect is learned. It's experience.
Use your pencils. When you're not sure, ink the outlines...leave your line art like little more than a coloring book and then go back in and shade in with the pencil the areas you believe would be touched by shadow or should be black for other reasons. Step back, take a look, and if it looks good then ink it and move on.
Tools. The paper you use is important. Paper with less "tooth", paper that's smoother, will bleed less...but can take longer for the ink to dry, so be careful not to smudge it. In the beginning, it's not unreasonable for inking to take even twice as long as it took to pencil. These are your absolute finished lines, so unless you're going for a rough visual, you're going to want them to be as crisp and clean as possible. Use flexible curves or ships curves or templates, inking compasses and rulers as much as you need to. Be patient, your speed will improve.
In the world of inks, "permanent" really isn't. If you want to keep the art for an extended period of time, you want to use acid-free paper and "archival" quality inks. ZIGs, Pigmaliners, Microns are all archival. Sharpies are not. Unless Sharpies have changed their formula in the last couple of years, they're solvent-base (that alcohol smell), and that alone will damage your paper. You can write on CDs with them because they eat into the surface. If it does that to CDs, think what that does to paper. Not to mention they aren't lightfast, and over time will turn a brownish yellow or purplish and fade out. If all of that doesn't stop you from using them, they also can continue to bleed out into the paper fibers for years, fuzzing out your original art over time.
Pigmaliners and Microns come in various tip sizes and while they are classified as "tech pens" they aren't the high end tech pens (which in this case is good) because you can force weight out of them with pressure. The higher end tech pens, like the Rapidographs and Rapidoliners have steel tips and hairs, and you really can't get any line variation from them. ZIGs come in various tip sizes and styles, including chisel and brush tips. All three can be found in just about any art store or craft section, and are frequently used for scrap booking, so they may be with those supplies as well.
For brushes and quills, I recommend FW acrylic ink or Dr. Ph. Martin's Bombay Black or Black Star.
I can go into further detail about quills and nib selection if anyone wants. Brushes, I've never been a brush inker, so mostly I just use brushes to fill or "spot" larger sections of black that are easier done by brush than pen.
Here are a couple of my own older pages I dug up where I found pencil scans before inks for comparison. These use a combination of pretty much all inking approaches I mentioned: