In my opinion to become a great fighter (as well as building on the Triangle hypothesis: technique, power, and speed) you must be skilful in long , mid, and close-range combat and ground fighting.
By long combat I don’t mean metres away from you opponent using guns and ninja stars. Instead, I mean an adequate fighting distance, i.e. before someone invades your personal space. This often tends to be around two metres. Since, most people’s legs are longer than their arms, I suggest a kicking martial art (and obviously from my background), I recommend Tae kwon-do (TKD). One aspect of TKD is learning how to cover distance (by stepping behind, skipping, and jumping etc), which is ideal for long range combat.
For mid-range combat, legs may be ineffective, so I suggest the use of hands through Boxing. Boxing will not only improve your punching power, but agility and body movement.
My choice for close range is a mixture of Muay-Thai and Brazilian Ju Jitsu (BJJ). Once in your opponents comfort zone it’s important to strike as fast as possible without big lavish kicks and spins. Elbows and knees can be effective blunt tools of destruction. However, most close range fights get tied up in clinching or/and go to the floor. That is why I propose BJJ.
So to summarise, I recommend TKD, Boxing, Muay-Thai, and BJJ as key martial arts to learn in becoming a great all round fighter.