Personally I see a "perfectly rounded" fighter is based on 3 different martial arts, although in all honesty "the more you know the better": Muay Thai, Jiu Jitsu and Tai Kwon Do.
Why? Simple. Muay Thai is the basic "standing-melee-fighting" style, well rounded, very versatile, no bullshit acrobatics. Simple, clean and very effective. Jiu Jitsu for the grapple-based fighting, specially ground-based grappling. In a 1 on 1 fighting it's quite possibly the most effective style. Also particularly good if you're at a significant size and strength disadvantage. And finally TKD, because acrobatics build agility, and TKD also teaches a lot of where to hit your adversary for maximum damage/injury.
Master those 3 arts (...goodluck with that...) and you're very likely to become very close to a perfect fighter.
-----------However--------
...It's somewhat insane to consider your average person will learn, or need, all of that. So if you really just want something you can do as a sport and to use for self-defense, I'd recommend wrestling (not WWE, actual wrestling), Muay Thai or Krav Maga.