Allow me to cut in.

One of my two planned characters is, in fact, a Human - and I am angling for them to have a rivalry with another character, in a vein similar to that of the rivalry between Vegeta and Goku.

The fact of the matter is that there are only four functional differences between Saiyans and Humans:

Zenkai, Ozoru, Transformation States, Higher Innate Power Level

Krillin and Tien both sort of plateaued in power during the Android Saga, but just by looking at the time Vegeta and Trunks spent training in the Room of Spirit and Time, there is no reason to think that a Human could not train similarly and gain a similar degree of power if they started from the same starting point (keep in mind that neither Vegeta nor Trunks regularly used their transformed states during the training period, unlike Goku and Gohan). 'Similar' in this case being frequent sparring and combat with other beings of approximately the same or greater power. After a certain point, working out and wearing weighted clothing stops being effective. If the Humans had spent more time frequently fighting with the more powerful Z-Warriors, they probably could have continued to increase in power - but because they started off so far behind and never even attempted anything like that, they were simply left behind.

There are likely other ways besides fighting others to increase your power even after regular training stops being effective, but all of them are likely dangerous and not something a Human would ever normally contemplate doing - Vegeta training in 500x Earth's gravity comes to mind. A Human with a high enough power level could have done the same, but the idea is so ludicrous you would have to be an idiot (Goku) to even think of it in the first place. Vegeta only got the idea after hearing about it from Dr. Briefs, after all. A Human is particular probably would not have pursued such an idea even after hearing about it. Especially since most Humans simply would not have the drive to become more powerful.

For a Human to attain power on the same level of the other species, they would probably have to possess an especially potent will, a good reason to do so, and the right circumstances.