Go with MMA. A good MMA gym will teach you everything: stand-up striking, ground game (ground & pound, BJJ submissions), and grappling. That's all you need in a clean fight.
If you want to learn one thing at a time, I would suggest Muay Thai for striking, and BJJ for groundgame. Just keep in mind that almost all street fights will end up going to the ground.
I was over 20 when I started Muay Thai. I tried Karate before that, but didn't like it because of all the katas (sequences) we need to memorize. Muay Thai is simple and effective.
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