I'd want to do some research before making a serious answer, but firing from the hip, not in order:

• DND 5e. It's the big one. Even if you don't like it, it's popular. If you're going to learn about a hobby you should learn what's popular in it.
• a white wolf game like Vampire. This was also pretty popular. It's got dice pools, no levels and classes, and themes that are more than "get treasure"
• a pbta game. They're popular now and typically have a very different feel from DND. I'm not sure which one to pick but there are many.
• one of those one page games, where you have like two stats. I don't like them but it's a good exercise to show what's possible.
• some other indie game with an unusual mechanic, like drawing tarot cards instead of dice, or using a Jenga tower.