Reddit reviews Muse - Piano Songbook

There's an official Muse piano songbook that includes several of the songs on your list (Space Dementia, Apocalypse Please, Feeling Good, Sunburn, B&H) as well as several others.

If you want to invest $10-$20, I recommend getting the Muse Piano Songbook. It contains 22 of Muse's more piano-heavy tracks (up through The Resistance album), including several of the songs that you mentioned.

The songbook contains both the chords and sheet music. Personally, I would start with learning the chords (and chord inversions, by extension). Sunburn, for example, may sound intimidating, but it's really easy once you discover that you're just arpeggiating^(fun word!) three chords over and over. Once you're comfortable with the chords, you can use the sheet music (or your ears) to nail the specifics.

As far as songs go, I agree with the consensus that Feeling Good and Sunburn are good starters. Exogenesis 3 isn't bad either. Explorers is also great, though the book doesn't have it :(

Of course, learning through YouTube will achieve mostly the same effect, because they're also going to break it into the chords and go from there, but it's always nice to have music that you can hold in your hand.