Software for Project/Product Management

Asana.com, recommended by Veronica Yanhs and David Bordow

As a biz operations consultant focused on efficiency and productivity, my recommendation for handling several simultaneous projects like your scenario would be Asana (asana.com). It's super detailed, collaborative, cuts down on email, and allows you to always know who is assigned to what task/how much of overall project is completed. It's free, and as you add more people (15), then it turns into a paid version.

I manage my 3 businesses using the free version and it is robust as robust can be for me. My teams stay on top of everything, and I have both a high level and detailed view of everything depending on what I want to see. I've customized it to fit my needs, so that at any given time, I can see every single task from every single business in one view. It helps a lot.

Google Docs, recommended by David Northway

After six different startups, you can not beat a simple, shared, task list in Google Docs for price and convenience,...(along with Google Calendar). Create a project task list in Sheets, and project calendar in Google, share with team and outsiders as needed. GoPro did this for first five years.

Eargo is doing this now with team of ~7 folks on dev team

JIRA/Confluence, recommended by David Northway and Juan Bruce

Once your team and number of projects exceeds ~10 people and 10 projects, then you can look at tools like JIRA/Confluence

Trello, recommended by Juan Bruce

I've found https://trello.com useful for a variety of projects and just organizing life.

Books on Management

Critical Chain by Eliyahu M Goldratt, recommended by Dave Maltz

For a cheap and fast way to get some ideas at a high level, I'd suggest reading Critical Chain by Eliyahu Goldratt https://www.amazon.com/Critical-Chain-Eliyahu-M-Goldratt/dp/0884271536. It's a fairly easy read in novel form that touches on some pretty good conceptual ideas for projectmanagement in an accessible way. It's certainly not enough by itself, but it's one good arrow for your quiver.

anything by Scott Berkun, recommended by David Northway

For books, anything by Scott Berkun is great for PM101