Tight, clean, pen and ink drawings.
Trace in Illustrator.
There are tools such as DynamicSketch that make actual drawing, by hand, with a tablet, possible in Illustrator. Using these it's very easy to retain the overall "randomness" and line vocabulary of hand drawing.
I'll point out.... You don't need Dynamic Sketch to draw in Illustrator. It's not "required" by any means. Illustrator has tools (Brushes) which allow you to draw in a more freestyle manner. Dynamic Sketch just makes it so much easier and better, especially if you are seeking a more "natural" feel. I'd suggest experimenting the Brushes in Illustrator first. And then perhaps try the free trail of Dynamic Sketch if you are finding brushes too limiting in some respect.
A drawing tablet is kind of required though... you can try with a mouse/trackpad/etc and AI brushes. However, in my experience it's exceptionally difficult to get any sort of "natural looking" drawing done with those tools unless you spend twice as much time refining after you've created strokes/paths. But in all fairness, there are those that can draw with a mouse exceptionally well. I'm simply not one of them.
Adobe's Draw app for tablets is also a possibility. It mimics much of what you can do on a desktop with Illustrator brushes.... but you get the benefit of the touch and "finger drawing". I, personally, don't like it for how I draw.... but you might try experimenting with that if you have an iPad/tablet. It saves vector files you can then open in Illustrator.
Everything in that last link has been "vectorized" in my opinion. The first link is behind a login wall. I know it's odd, but not everyone uses Instagram or finds a need for an account there.