First of all, awesome to hear someone else is running games for kids at their local library! It's great to hear about someone taking on the role of an ambassador for our hobby.
I currently run a game at my local library for a revolving group of about 15 kids (typically about 9 show) so I am very aware of the difficulty of keeping things moving fast and and keeping the difficulty low.
The first thing I did was use the Pre-Made characters pulled from this site:
http://www.tabletopping.net/dd-5e-pre-made-characters.html I pulled levels 1-10 for every single one and had the kids choose their favorites. That way when they level up they simply grab the next character sheet. Some of the kids have since graduated onto making their own characters and I simply inform them that if they really want to do that they just need to have that character ready for game that day.
I play fast and loose with the rules some. For me this is about introducing the game to these kids, if they get really attached to it and start running\playing in other games they can then get really invested in the rules. I'm up front about this to them, I've let them know for instance that I'm leveling them up on a "this feels like a good spot for it" basis rather than keeping detailed notes on 15 kids point values. It's important to me that they know this game can get much more complicated if they want it to.
For combat I've been using a lot of gridless combat. It speeds things up dramatically. I've demonstrated using the grid though.
A few other tips I've found useful:
- If a kid wants to bring a different character every week, I typically let them.
- Have your library purchase one or more PHBs for the kids to use. My library has a bunch of RPG books on hand now.
- Document your successes, I'd love to hear about them
- Here is a link to my blog, specifically the page where I've stored articles I've written about this stuff:
https://melsmifgames.wordpress.com/volunteerismadvocating-the-hobby/