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1. Palpatine
2. ?

Dooku

Jar Jar beats both.

Marr?

Palpatine's political power doesn't actually stay in his ability to influence people directly, but rather how he manipulated others to manipulate people directly.

Krayt, maybe.

Amidala was unnaturally gifted, but I don't know if I'd put her up as the best, by any means.

Dooku or Tarkin, imo.

thrawn?

Hard to say.

In the Thrawn novelization it was stated multiple times(by multiple characters) that Thrawn isn't very politically astute... But that's mostly because he is a warrior/military tactician, and has no will or motivation to play the ridiculous games of politicians -- he is blunt and to the point, and most politicians didn't like that(they wanted their asses kissed.)

That said, Thrawn's tactical outlook allowed him to see even the most minuscule political weaknesses/flaws of the Republic's(and Empire's) governmental infrastructure. In his discussion with Nightswan, Thrawn made it clear that he had a vision of the ideal government in mind -- one more cohesive/unified than the Republic, but less tyrannical(and more democratic) than the Empire. He also knew that the tone of a government is set by its leader, and planned to use his position as a high-ranking senior officer to help select a more appropriate ruler for the Empire when Palpatine eventually died.

So even though politics may not have been Thrawn's main area of expertise/focus, he clearly had a substantial political endgame in mind -- one that sounded pretty damn impressive, tbh. Frankly, if Thrawn would have been allowed to revamp the entire governmental superstructure as he saw fit, I think he could have done some truly amazing things... But that's neither here nor there. /shrug

Bail Organa

In other words: Thrawn should have been 'Vader'

Regarding Dooku's political aptitude, I just remembered this:

https://i.imgur.com/3nb3BrV.jpg
-Vader: The Ultimate Visual Guide

Dooku is the obvious answer, though a large part of it is his pedigree as a master Jedi and member of one of the richest and most powerful families in the galaxy.

Legends
1. Darth Sidious
2. Darth Vowrawn (assuming he doesn't die like Acina did)