First of all, I assume you are looking into IT product management.
From what I've seen the PM role differs at each company in as to what they require skill-wise. But here are some recommendations based on my experience.
First of most of the job boils down to having good communication, story-telling and negotiation skills. A great place to start off with would be this Coursera course and pick-up the book Never Split the Difference - Chris Voss.
Even though you might not see yourself as "code monkey" it is really important to understand technology well. A great course to start off in this regard would be CS50.
Then it would good to pick up some design skills. Read books like Don't Make Me Think by Steve Krug and Design of everyday things by Dan Norman. You can also check out the course UX Fundamentals by Aquent Gymnasium. Then I will recommend doing the weekly design exercises. Remember the goal is not to be pixel perfect but rather how to think design.
Then you can check out books like Four Steps to Epiphany - Steve Blank and Inspired - Marty Cagan.
Also, the course Digital Product Management by Alex Cowan is a good introduction to product management. Also, this Udemy course Become a Product Manager by Cole Mercer and Evan Kimbrell is okayish.
I will also recommend to pick out your product and do a case study on it and think of ways on how you can improve.