I highly recommend "80/20 Running: Run Stronger and Race Faster By Training Slower" by Matt Fitzgerald. Don't let the title put anyone off -- it's about performance, but most of the book is about the value of going SLOW.
Like you, I was never really a runner, although I did get into running when I met my current partner, who is a runner. I think what's complicated for most not-fit people is that they only have one running "speed'. I only had one running speed until I was almost 40. There was walking, and then there was running. Obviously there was also "sprinting" but we all recognize that's unsustainable. I think for most of us, "running" is what a runner would call a tempo run -- say 80% of your maximum heartrate, something you feel you can sustain more-or-less indefinitely, but that's hard.
When you're not-obese-but-out-of-shape, you might walk a mile in 15-17 minutes, and a run would be in the 10-12 minute range. It's hard to actually go any slower than that and still be running. And as you slowly get more fit, your runs get down to (say), a 9 minute mile, an 8 minute mile. But you never realize you can (and should!) scale back to that 10 or 12 minute mile. You'll be able to run every day instead of every few days. You'll get the health benefits without the injuries. And the side benefit is that, if you add speed work, you'll get faster more quickly than if you just ran at 'running speed' all the time.
The couch to 5k program listed mentions mixing walking and running -- this is a great alternative to a "slow run" for those who still only have 1 speed.