Disclaimer: I don't own the Dragon Ball franchise or it's related concepts and characters, but Akira Toriyama and his affiliates do.
A Saiyan Warrior's Heritage
Pilaf's Castle, Mushroom Forest, Diablo Desert, Mount Paozu, Earth, Universe 7, Age 749, September 9
Upon defeating the Pilaf Gang, who were then tightly bounded with rope, so that they could be turned over to the law, Goku and his friends, Bulma, Yamcha, Oolong, and Puar, were able to gather all the Dragon Balls. However, seeing how it was Goku who brought them thus far and that their desired wishes were mostly self-serving, the others decided to let Goku make his own wish. After thinking it over and remembering everything that he and Bulma were able to learn about himself by far through the latter's scientific knowledge and their joint discovery of the space pod near his home, Goku decided that he wanted to wish for more knowledge about himself and where he came. And he figured that the best way to do that was to see if he could meet more people like himself.
"Eternal Dragon Shenron!" Goku said to the entity of the Dragon Balls. "I wish that I was able to meet people just like me from all over this universe and beyond! Can you do that?"
"As you wish." Shenron rumbled as a large glass cube with leg attachments at the bottom then appeared in front of the team. "What you see before you is what the Gods of the Multiverse refer to as a Transport Cube used to allow free travel across this universe and the remaining eleven. It has already been installed with the Ki signatures of the Saiyans native to our world of Universe 7 followed by the Saiyans of the universes that have them. Your wish has been granted. I'll take my leave."
As the Dragon then disappeared in a form of light, Goku quickly grabbed the Four-Star Dragon Ball before it and the rest scattered all over the Earth before he then set his sights on the Cube.
Planet Sadala, Universe 6
After initially using it to find others of his own kind in his home universe, Goku decided to look elsewhere for Saiyan companionship after reasoning that his species in Universe 7 was both unpredictably hostile and endangered. Therefore, he arrived on the Universe 6 version of the original Sayian home world, Planet Sadala, which had a nice jungle environment that reminded him of home. From what information the Cube provided about Universe 6, Goku understood that it operated on a different time zone then back home. One year for Universe 6's inhabitants was five years for Universe 7's, but he hoped that he could find a teacher that he could come back to every now and then, which led him to explore his surroundings a bit before he was soon found by two local girls around his age.
"Who are you?" The shyer one in red asked him.
"And why do you have a tail?" The bolder girl demanded of him. "Last I checked, Saiayns evolved past the point of having tails."
Goku smiled widely at them before replying. "My name is Goku. I'm a Saiyan from another universe. What's your names?"
Although they didn't appear convinced by Goku's statement of where he came from, they quickly said that their names were Kale and Caulifla.
Was prompted to write this after reading Goku's True Heir by Devlin Dracul on FanFictionNet. Honestly, I was pretty disappointed as I was reading through about the way Chi-Chi was being treated in favor of Caulifla as well as that they wanted to break up Goku's family, so that they could pair him up with a Saiyan girl that, as far as anyone knows, may be younger than Gohan in age. I'm good with pairing up guys with girls that are three, maybe even four, years younger than them, but I put a stop after that for obvious reasons, especially if the girl in question is old enough to be the guy's daughter or granddaughter. However, Devlin Dracul used to lend me an ear frequently once and I didn't want to be on bad terms with them, so I hope they find this interesting if nothing else.
I know Chi-Chi is not the perfect wife for Goku, but then again, what is 'perfection'? After all, if the fandoms we're into are perfect from the start, then fanfiction wouldn't exist, now wouldn't it? Nonetheless, I'm pretty much convinced that those two do indeed care for each other and I actually hate the idea of breakup fanfictions, especially if there are kids involved. It might as well be a melodramatic soap opera which is as distasteful as it sounds.
So, here's my advice for those who want to give Goku a different girlfriend/wife in their own works: look back at the beginning. There's a reason why the type of fanfiction I'm most inclined towards is called 'Alternative Universe', if you know what I mean. Granted, it would mean watching/reading the Dragon Ball media as a whole, but with the right vision and commitment, anything can happen. Just thought I'd get that sorted out.
Sorry if I didn't send a lot of information in this that made sense to you all, but I promise that I intend to forego the one-shots completely, so that I can write longer stories at the end of the year and onwards.