What kind of side projects would you like to see from someone interviewing for a JavaScript (front end or backend) related role? If they started with tutorials but did something different is this okay? I also want to start something small, so I can stick with it, but I don't want it to be too small or lack complexity. Thoughts?

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Having a Github repo that has more than a few stars or shows a lot of traffic would be impressive; it shows you solved a problem other people have and did it well. It doesn't really matter what it is. Having a merged PR on a popular open source JS repo would be good too- shows you can work with other people's code and (likely) follow style conventions.

Projects someway related to the role your interviewing for would probably be best, however I find anyone that has any type of projects to show is giving a much better impression to the interviewer. Ensure the projects are well structured, have clean, good quality code that is well documented. Rather that following a tutorial, take something and try to recreate it, or think of what you do in your day to day life and see if you could create something to improve it. I'd be against following tutorials for the purpose of creating demo projects for an interview, if your following a tutorial, it's not exactly your own work.

IMO, you should be able to explain why you wrote any particular line of your code. Also, you should be able to discuss the pros and cons of your approach vs other approaches. This will ensure that your project does not look like a "copy-paste" job.

For me, it would be the ability to work with various libraries, knowing why one is better than another, and also the ability to write your own library if what you want doesn't exist.

Libraries of interest to me (as front-end hirer) would be things to do with DOM manip, SVG, Animation, WebGL, generative visuals (particles etc), WebMIDI, device gyro/accelerometer, touch/gestures.

I guess the most important trait is that there is a natural curiosity and it shows in the work, even the dead-end projects matter imho.

Thanks for the advice!