With respect to the Phantom Menace and Palpatine's Plan, you are wrong.
Essentially all we miss is how he went from Senator of Naboo to Chancellor of the Senate and his initial efforts to goad the Trade Federation to War.
But really, we don't know how he got to be a Senator from Naboo, or positioned to be the first choice for Chancellor... and as far as II and III goes, we don't really care about the Trade Federation. They are just one of a half dozen or so factions of the Separatists at that point.
Because, ultimately, TPM is a fucking mess of a movie with just plain bad choices that had people scratching their heads up and down. Amidala's falling for a kid much younger than her (or alternatively, being insanely young to be elected queen of anything other than the corn dance...), the pointless introduction and death of Darth Maul, the pointless introduction and death of Qui Gon Jin (seriously, I can't find a single point he made about its exclusion I don't agree with, and I'm willing to tack on more regarding the sheer harm it does to the narrative flow of the arks presented!... not least of which, from the entire point of the question (how do you show all of these to a newcomer so that it makes maximum sense?) it subtracts substancially from the narrative arc by destroying parallels built by its exclusion.
Your dissection of Palpatines plotting is certainly insightful, portraying him less as a master manipulator and more as a masterful opportunist, who happens to be a SKILLED (rather than masterful) manipulator... which might also help explain his utter failure with Luke at the end...
But again: We can always go back further, find more details. Who trained Palpatine, how did he decide on politics as his avenue to destroying the Jedi, what was he like as a young man???
We have some fifty years of backstory on the Emperor that is just missing. Excluding a few months, no matter how interesting or key to his plans from a decade back won't hurt.
Honest.
And this way we can ignore Jar-Jar for free..