When you follow artists on Instagram or YouTube, or take online workshops from creatives, you'll see there are a few brands of pens recommended over and over again. I regularly hear about Microns, Uni, and Faber-Castell.
While every artist has their preference, I've been using the Micron Pens because it's what I have on hand—and so far I haven't had a reason to try another brand. They come in a variety of sizes, feel comfortable in my hand and make smooth lines. Maybe as they start drying out I will give another brand a try, just to compare.
I have the following sizes which came together in one pack: 005, 01, 02, 03, 05, 08, 1, and Brush.
The recommendation Lisa Congdon gives in her line art class on Creativebug is to start with a larger tip for more control as you're learning: size 08 or 05. Each size can each be used for different things: 01 for small details, 08 for filling in areas that need to be fully black, etc. but lately I've been gravitating towards the thinner tips when I sit down to draw. There's a daintiness and simplicity the thinner tips give that I like...at least for now :)
For comparison purposes, here is a similar drawing using six different pen tip sizes (005 is smallest, 08 is thickest):