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Sakura Pigma Microns
A lot of my students use these. The last time I used them was when I was in high school, and at the time I felt that they dried out pretty quickly, though I may have simply been mishandling them. As with all pens, make sure you're capping them when they're not in use, and try not to apply too much pressure. You really only need to be touching the page, not mashing your pen into it.
In terms of line weight, the sizes are pretty weird. 08 corresponds to 0.5mm, which is what I recommend for the drawabox lessons, whereas 05 corresponds to 0.45mm, which is pretty close and can also be used.