Welcome to the forums! Your thread title caught my eye. I like your philosophy :)
I'm a reformed fish owner, too. My mom thought she knew what she was doing (thanks to the local fish store) and I learned through her. Many failed attempts later, I realized that maybe I wasn't cut out for fish keeping. Fast forward to today, I have my own daughter and have come to realize just how uninformed I was. I'm about to undertake fishkeeping again, this time with knowledge!
Anyways, just had to share that you're not alone in having done the wrong things. The fact that we're here to try and make it better is a great step!
If you can go a bit bigger than a 3 gallon, the Hex 5 gallon is really good:
The size is vertical versus horizontal so it may fit your size constraints.
Because it's bigger, there's room for a buddy in the tank for your betta (as OFL says, only a shrimp and/or snail qualify). Lastly, it's also only $5 more than the 3 gallon. Win!
Whatever you choose, just make sure you get a quality heater.