I'm not here to try and teach you how to draw with ink. Thank goodness for that, as I'm a digital artist myself. I have chosen these kinds of pens however because they complement the lesson material and the concepts being covered, and more than anything, they help encourage the kinds of habits and respect for your linework that goes hand in hand with everything else I am trying to teach. I explain this in greater detail in this article, "Why Ink?".
They do that by producing a rich, dark line regardless of how much pressure you apply - their only dimension of variance is in the weight of the stroke. The 0.5 size for most brands is ideal, as it allows for a great range of weights. I do not want you to use different pens in the same drawing - don't go drawing in a 0.3 and then going over it with a 0.5 or anything like that. Ideally if you can, pick up the 0.5's in bulk.
If you can't find a 0.5 specifically, anything from 0.4 to 0.6 will do, but I wouldn't go outside that range if you can help it.
Aside from that, the brands I've used include Staedtler Pigment Liners and Faber Castell PITT Artist Pens (their sizing is different, F is the equivalent to 0.5), but you're not limited to these. There are many other brands, ranging from Copic Multiliners to Sakura Microns and hell, even Sharpies (the Sharpie Ultrafines and the Sharpie Pens) will do.
Just make sure that when you're drawing with these, that you're not applying too much pressure. Students have a tendency of damaging their pen tips this way, which reduces the flow of ink and forces one to draw with the pen held at a higher angle to achieve the same rich marks. Most think that their pens have just died, but these things can actually last for a good while, even with all the drawing that we do for these lessons.
That said, do expect to end up buying quite a few if you're in it for the long haul, from lesson 1 to 7. Pens can get a little pricey, so find a brand with a price point and quality balance that works for you.
Note: In an effort to help students access more reasonably priced fineliners, we do periodically import and sell them ourselves. They're not always in stock, but they're roughly comparable in our experience to Staedtler Pigment Liners (my pen of choice), and in our testing, one has lasted us through all of Lesson 1 and halfway through the box challenge before showing any signs of wear. We sell them in packs of 10 for $17.50, and you can learn more about them here.