I just checked showconfig, and it says my kickstart is 37.1
Thank you for all the replies !!!
That's Kickstart 2.0 (which explains why you have Workbench 2 to go with it).
I'd still upgrade to 3.1 if I was you. A Kickstart update is the first thing I do to an Amiga when I buy it.
As for games, most games for the A500 should run, just don't expect to do much 3D rendering in Lightwave.
I know you don't want to spend money on hardware, but keep an eye on eBay for a cheap 68020/030 CPU card. They pop up from time to time and then your worries will be gone and you'll be able to run OS3.1 and WHDLoad.