I did boxing for a few years.. Very interesting sport, but in my opinion there are better ones. MMA is definitely a good option if you want a range of things rather than just a specific area.
For self defense, I'd hands-down suggest Krav Maga, however that isn't competitive so if that's what you're looking for, look elsewhere..
There are loads of other martial arts, they all offer something different.. You could always go for somethign traditional such as karate kung-fu or karate, or go for something more westernized like boxing (as you originally mentioned) or kickboxing.
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