Freeza requests he goes to see his new 2nd-in-command's planet, with him then attacking Earth's population and telling Goku he only said he'd spare his friends and family, not the other inhabitants. How things go depends on whether or not this injustice is too much for Goku to tolerate.
1. Goku attacks Freeza and is ultimately killed along with his allies. Freeza then wipes out the Earthlings and sells the planet to one of his business partners. One of the few survivors is Gero due to his secret laboratory not being found (and his top tier gate shielding him if Freeza attacks the mountain range). With his enhanced data, the Artificial Humans are far stronger than in canon and Gero has no trouble killing Freeza after drawing his attention to Earth by killing its new owners and taking his spaceship for experiments. He then goes into space with #19, overthrowing the Cold Empire and establishing the Red Ribbon Empire in its place, enslaving many for scientific experiments and energy supplies. His reign would go undisturbed unless he either catches Dabura's attention or finds Broly, with him being easily killed in either case.
Meanwhile, Cell develops into adulthood decades later and achieves his perfect form without issue. He then destroys Earth and flies into space. He'd eventually encounter Dabura and fight against him. For the sake of avoiding the whole Dabura VS Cell/SSJ or SS2 Gohan debate, I'll just say that the battle goes one of three ways:
A. Dabura spits on Cell and Cell is unable to counter in time. Babidi likely never amasses enough energy to revive Boo and would be killed by Beerus whenever he chooses to wake up.
B. Cell falls under Babidi's control after proving his strength, becoming a highly efficient subordinate. It takes Babidi far more years than in canon to amass the energy for Boo and he has to scour the universe (and all of its 28 inhabited planets

) for energy. If Shin gets involved, Cell or Dabura easily kill him. Either Babidi rules the universe for as long as possible or Boo's dangerous nature cause Cell and Dabura to fight against him. In the latter case, the teamwork of the two is enough to stop Boo due to Cell's techniques and Dabura's spit creating an opening. Babidi is annoyed, but sees that perhaps his new subordinates are more useful than Boo would have been. Babidi rules the universe for however long he may live, unless he visits Vampa.
C. Cell gets a big enough Zenkai to kill Dabura and Babidi. Cell goes unchallenged until visiting Vampa and fighting Broly. His Zenkai abuse eventually allows him to reach Broly's level. Beerus wakes up when sensing two people in the mortal realm with power on par or superior to his and goes to challenge them to a three-way match. Beerus eventually wins due to superior skill, but appoints the two as Hakaishin candidates, Cell being the one to become his successor if Zen-Oh doesn't erase Universe 7 by that point.
2. Goku sits by and tells his allies to do the same. He willingly serves as Freeza's right hand and is tasked with taking over other planets. A few years later though, he dies to the heart virus. #17 and #18 cause chaos on Earth and with no Trunks in this timeline, Gohan is more vigilant and level-headed about attacking them. Bulma eventually builds the time machine and he travels back to a day before Goku took off for Namek. Once his father is healed, Future Gohan informs him of everything and goes with Goku to Namek in order to train him to become a Super Saiyan. Goku is able to do so by the time he arrives and Gohan lets history play out the same until Goku VS Freeza. With the knowledge of what will happen, Goku decides to show no mercy to Freeza and begrudgingly kills him. Future Gohan then gives him the heart medicine before returning to his timeline. Things go the same as in canon with Freeza's victims being revived, Trunks being born, etc.Without Goku learning Shunkan Ido, however, Cell destroys the Earth with his self-destruction and then goes into space to fulfill one of the scenarios in the previous branch.