And by that, I mean I wouldn't make it Super Saiyan at all. The Super Saiyan form, as we know it in my concept, is a false one, a transformation created by the body to compensate for the fact that the Saiyan lacks a tail, and thus an output for their most bestial, primitive nature. True Super Saiyan would be only accessible by the Legendary Super Saiyan, and be the one true all powerful Saiyan, as it was always described to be, a power that put fear into the heart of Frieza, not something that even small children could master or be gained through back tingles in a poor attempt to use chakras, much less "S Cells."
So we have true (Legendary) Super Saiyan and false Super Saiyan as forms. Legendary is locked to Broly, or whoever you want to use in place of him in whatever canon regardless of having a tail, but false Super Saiyan is only accessible to those without a tail, and thus lack any access to the giant ape transformation. Because of this lack, a Saiyan cannot express their true, primitive nature, much less have a power boost that is inherent to the species. As such, the path to false Super Saiyan starts with rage, one of the most base of emotions, something that Saiyans tap into on a daily basis in combat. Goku would basically gain the form as he did normally, through the power of his rage and desire to hurt Frieza. His primitive Saiyan nature would overcome his normal personality and manifest his Saiyan base nature, his body increasing its power output like he was transforming into a giant ape, however it would be contained in his humanoid form. Hence his muscles would expand and his power would increase, but because he does not change into a far larger form, it becomes more compact and thus amplified, hence the massive power boost compared to the giant ape form. So much power would be produces, as a matter of fact, that it would leak from his body, giving him both the aura and change the way light was reflected off of his hair and eyes, giving them a different color, or even that the energy pouring out gives them a radiance in those colors.
Frieza and Vegeta could still both believe it to be THE LEGEND, even though it isn't. If we take it at face value, true Legendary Super Saiyan is the most powerful thing ever, it's enough to simply beat everything. The Super Saiyan forms we see later on are proof that this is some kind of falsehood, as they keep growing in power and are different forms, a far cry from the one form to rule them all. Even Broly says that his ki kept increasing during combat, and in the second film, a zenkai boost was all he needed to put him on the level of a Super Saiyan 2 Gohan (and yes, he was in Super Saiyan 2 even without the electrical bolts), rather than him gaining some kind of Legend Super Saiyan 2.
The series would go as normal, Vegeta would get it, Future Trunks and Future Gohan would have it, present Gohan would get it, just showing how it's not a truly legendary power if everybody can just get it. This is where things further change in my concept.
There are two paths that Super Saiyan took, and it fits in well with my idea. The second and third grades, dubbed Ascended and Ultra by the fans, are simply giving into the more primitive nature and trying to force more power out of it. They grow larger in mass in both cases because they are simply pushing more toward their bestial nature and a lust for combat, which is seen in Vegeta and Future Trunks doing it to beat Cell in raw terms of power. Goku sees through the flaws of Ultra, but on a more basic level in this, he sees the flaws of pushing toward the primitive, as it will forever dominate you if you give into your baser nature. Like in the series, Goku and Gohan go on to stay in the form permanently, harmonizing themselves with the power and controlling their emotions, overcoming their base instincts. With this, they maximize the power and have full mastery over themselves, thus Full Power Super Saiyan is the most complete False Super Saiyan form anybody could ever get in the series based on how I have structured it.
Gohan, however, is a special case. His power has always been the strongest due to rage. He has powerful emotions. In the series, he hits Super Saiyan 2 because of his rage. In my version, this is Gohan exclusive and based on his more powerful emotional state, and the fact that he goes from being in harmony with his primitive nature to being pushed deeper into it due to his extreme rage. He gets so angry that his power explodes, manifesting his true latent potential, which the franchise has hammered into our heads time and again that he has whenever he needs MOAR POWAR. This rage mode is so intense and his power so vast that his energy pours out in such a constant stream that electrical energy floats about him, almost threatening to consume him, just as his emotions and Saiyan nature threaten to consume his mind and ability to think. He becomes sadistic and cruel toward Cell, wanting him to suffer, and to further extend the fight to fulfill his desire for combat. He fights both Perfect (and later Super Perfect) Cell as his natures also fight, which is why Super Perfect Cell appears to be stronger. When he overcomes the Saiyan nature, all that held back power comes flowing out, allowing him to easily crush the bio mechanical bug man.
After this, nobody else can access that form. Full Power is the highest anybody can get. Super Saiyan 3 could appear as a continuation of the Ascended and Ultra line of thought, a deeply flawed form that burns energy like nothing else in exchange for temporary immense power that could reach, or surpass, Gohan for short bursts. Going further and into the land of GT, which I know everybody just LOVES, Super Saiyan 4 could be the idealized merger of both Saiyan transformations. Goku, through regrowing his tail, would gain access to the golden great ape, a form that isn't supposed to exist. It's an immense power boost, but again he loses himself in his own primitive nature, amplified by his immense power. When he finally overcomes it, like Gohan, he instead forces the two transformations to fuse and compress, shrinking down to a humanoid form, yet retaining traces of his bestial nature, showing the true fusion of two disparate transformations that should never be able to coexist naturally. It is a mutation, an oddity, immense in power but so easy to lose, as his nature must always be kept in check. It is, in essence, the nearest thing anybody else could get to the Legendary Super Saiyan who isn't the actual one.
Beyond that, nothing else exists. There are no God forms. That's stupid. Everybody knows they're already stronger than the gods, so why would they need a God form? How foolish.