Vegeta's redemption arc in Dragon Ball Z is the stuff of legends. The Saiyan prince went from a bloodthirsty killer to an anti-hero by the end of DBZ and is now a full-fledged good guy in Dragon Ball Super. While Vegeta's path to redemption wasn't overt until near the end of the Frieza Saga, it was in the preceding saga that the seeds for his character arc were first planted. After all, even Raditz killed more citizens of Earth than Vegeta in the Saiyan Saga.
Vegeta was introduced as a full-on villain in the Saiyan Saga, delighting in the pain of others and mercilessly executing his own comrade. Certainly not for lack of trying, but none of the Z Warriors who lost their lives against the Saiyans did so by Vegeta's hand. Surprisingly, Nappa is the only person that Vegeta kills during the Saiyan Saga. Considering that Nappa had just killed Piccolo after Tien Shinhan and Chiaotzu fell in battle against him, not many people had an issue with Vegeta taking Nappa's life.
It seems very possible that Vegeta was kept from committing any unforgivable crimes during his introduction so that his eventual redemption would be more accepted by fans later in the series. Even with Goku's forgiving nature and the power of the Dragon Balls, it would have been a tough pill for fans to swallow if Vegeta became part of the group after murdering other members of the group. It's much easier to forgive Vegeta when he only tried to kill them than it would be if he had successfully done so.
This is not to say that Vegeta's redemption was well underway at this point, as he did go on to violently slaughter an entire village of Namekians during the Frieza Saga. Worse, Vegeta was not a henchman of Frieza at that point, so the heroes' wish to Shenron didn't actually resurrect this village as it did all other Namekians who were killed by Frieza and his men. While there's been no indication that this village has ever been revived, much later in the Super manga Vegeta displays visible regret over his past treatment of Namekians.
There wasn't much to humanize Vegeta with during his introduction, so his redemption arc still had more than enough ground to make up even without having killed any of our heroes. It could even be said that the events of the Saiyan Saga pushed Vegeta even further away from redemption, considering his loss to Goku had him behaving even more mercilessly on Namek in his quest to gain power and immortality. But the fact remains that Vegeta's distinct lack of a hero's blood on his hands after his introduction hinted at much more story to tell for the Prince of All Saiyans.
Vegeta has come a long way throughout DBZ and Super, his days as a planet-conquering villain long behind him. Vegeta has even saved the lives of the very people he tried to kill in his introduction on multiple occasions. Though he now possesses the ability to fight for something other than himself, he's still as deadly arrogant as he was during the Saiyan Saga. The only difference now is that he defends the Earth and the universe from the very same threat he once posed himself.
