This order still focuses on the story of Luke Skywalker, but I put "Solo" and "Rogue One" before Episode IV, as that is when they take place giving good context to the start of Episode IV.
I also went ahead and removed Episode I from this list as it's not imperative to watch, but, if you wanted to, it would be watched after Episode V and before Episode II.
Episode I contains very little plot progression. Qui-Gon Jinn and Darth Maul are both dead and largely forgotten by the film’s finale (TV spin-off series notwithstanding) and all of the other characters — Anakin especially — are far more effectively introduced in Attack Of The Clones. The fact that a grown-up Padme no longer meets her husband-to-be when he’s nine also has the benefit of making that whole relationship a little less Operation Yewtree. So no Jake Lloyd (“Yippee!”), precious little Jar Jar (“How wude.”), no weird Amidala/Padme identity confusion and, crucially, no discussion of midichlorians, the introduction of which is without doubt the most egregious example of Lucas’ tampering. It also makes the ‘flashback’ shorter and less intrusive, improving the Rister model’s flow significantly.
However, it contains much that’s objectively terrible but there are also redeeming qualities. The three-way saber fight (set to the rousing Duel Of The Fates) is the saga’s choreographic high point. And, despite being entirely superfluous from a plot perspective, the podrace is an exhilarating sequence where George Lucas’ giddy youth as a teenage petrolhead really shines through. Equally, while the banishment of Binks might seem like the gods’ work, Jar Jar is an appealing entry point for younger viewers, responsible for some of the most child-friendly comic relief.
Beyond all that, however, there arenarrative points in The Phantom Menace that serve a purpose. The film sews the seeds of Senator (then Chancellor) Palpatine’s ascension to power through his manoeuvring to displace Chancellor Valorum and assume the premiership. Similarly, while widely loathed, Jar Jar is a narratively pivotal character as is he who is ultimately tricked (in Episode II) into proposing a motion to grant emergency powers to the Chancellor, paving the way for Palpatine to assume the mantle of Emperor. Without any character foundation, or understanding of his relationship with Amidala, Jar Jar’s role in the Empire’s formation loses weight.
Without Phantom, the prophecy that Anakin will bring balance to The Force is mentioned but never explained, and Anakin’s return to Tatooine in Attack Of The Clones is rendered baffling as we have no knowledge of him being a slave, who Watto is or why his mother has ‘been sold’. C-3PO’s origins also become murky but that’s hardly a major drawback.
Finally, the excision of Episode I derails Anakin’s prequel character arc entirely. Never seen as an innocent, we are introduced to him as a surly, sulking teenager with more than a touch of the Dark Side about him. Without the altruistic (if infinitely irritating) boy we first meet in Watto’s junk shop, Anakin’s rise to the mantle of Sith Lord is as unsurprising as it is undramatic. For a true redemption of the character, he needs to come full circle, so The Phantom Menace, however flawed, must remain on the menu.