Obviously, Vegeta’s weakest form is his base state. One would think he would never rely on this form, but there’s an advantage to using it. In Vegeta’s base form, there’s no drain on his stamina at all. And as a Saiyan, most people who will challenge him don’t come anywhere near his full strength.
This is why he tried to use his base form during the Tournament of Power because most people in it weren’t able to harm him.
Super Saiyan is the standard state used by Vegeta when he’s vaguely serious about a battle. It’s the level where he knows his opponent is a threat, but he’s still feeling out just how dangerous of one they actually are. He uses Super Saiyan in his battle against Cabba, where Cabba is impressed that Saiyans of Universe 7 even possess transformative abilities like that.
Of course, it’s far from his strongest state, and that’s why he teases Cabba by showing him the Super Saiyan God Super Saiyan transformation before knocking him out of the tournament when Universe 7 and Universe 6 were battling.
For a long time, Super Saiyan 2 was the strongest Vegeta ever got. The character never attained Super Saiyan 3 so he was always a form behind Goku. Vegeta first showed this form off during his battle against Goku in the Buu Saga, when he was Majin Vegeta.
In Super, he hasn’t relied on this form nearly as much. He needed it during the Battle of the Gods arc because that was the best he had against someone like Beerus. After Beerus slapped Bulma, Vegeta went into Super Saiyan 2 and surprisingly lasted even longer than Goku did in Super Saiyan 3. Still, once Vegeta surpassed this form it was rare he bothered to use it anymore.
Super Saiyan God is actually a form that Vegeta seemed to have skipped, much like Super Saiyan 3. When Resurrection of F happened, Vegeta was already in Super Saiyan God Super Saiyan form, and once it was obvious he had attained the highest transformation no one thought it necessary for him to learn the other.
In fact, in the Super anime he never actually used this form. He made his first appearance with this form in the manga, where he utilized rapid switching between this form and Super Saiyan Blue to battle against Goku Black. Vegeta wouldn’t decide to use this Super Saiyan form in the anime until the Dragon Ball Super Broly movie, where he gradually scaled up in power against Broly once he realized how much more powerful the exiled Saiyan could become.
This form represents equality for Vegeta. For years, Goku was always one step ahead of Vegeta in Super Saiyan forms. Goku had Super Saiyan while Vegeta had nothing, he mastered Super Saiyan 3 while Goku wasn’t aware the form ever existed. Even Super Saiyan God was something that only Goku had.
But in Resurrection of Frieza, Vegeta finally learned something crucial: train under the same teachers as Goku. He leapt at the chance to train under Beerus and Whis, and for his efforts he was rewarded with the Super Saiyan Blue form. He would also learn the limits of the form, as transforming into it and out of it frequently costs a lot of stamina in the manga, which is how he lost to Hit.
Super Saiyan Blue Evolved is a throwback to the Super Vegeta era of Dragon Ball Z. The form is very reminiscent to Super Saiyan Second Stage, where Vegeta’s muscle mass increases drastically. This form originated in the anime, as Vegeta needed to find a way to attain a new level of power to compete with Goku, who was using the Super Saiyan Blue Kaio-Ken technique.
The two of them together weren’t enough to defeat Jiren, and so they both had to break past their limits to stand a chance at even moderately equaling with Jiren. Though the form looks largely the same aside from a more sparkly blue aura, both the gods watching and Jiren note that it gives Vegeta a massive increase in power, enough to stand alongside Goku with his Kaio-Ken multiplier combined with Super Saiyan Blue form.
Ultra Ego is definitely the most accurate power-up Vegeta’s ever attained. While Goku chose to train under Whis to learn Ultra Instinct, Vegeta’s mindset doesn’t allow for him to learn something like that. Instead, Beerus decides to teach him so that the techniques of the gods of destruction don’t lose to the techniques of the angels.
The form gives him a brow similar to that of a Super Saiyan 3, and changes his hair and aura color as well. This power-up brings a lot of advantages, but it’s also incredibly dangerous—the form is only achieved by being hurt considerably, and Vegeta continues to gain strength as he takes damage during the battle he’s in.