How do I know what I have and what would be compatible with it?
The best thing to do is go down to your local shop and have them take a look, they can also help you with new wheels.
If you want to DIY the measurements you can use this from the late great
Sheldon Brown
https://www.sheldonbrown.com/frame-spacing.html
You will know if you have a thru-axle if it is as described above. More than likely it is QR but double check don't just believe what is said know for yourself.