Hi and welcome!
For those styles I would go with something vintage. That should give you all the glorious cleans you need for that and since BKPs are great they will also easily handle all the gain you need. Depeding on which Muse songs you play those should be the most extreme sounds but could be handled too.
Of course the recommendation is to a certain extend also dependant on which guitar you have, so a comment on that would be cool, but I would say you can hardly go wrong with a Mule with Mothers Milk. The Mule is the gold standard `59 Humbucker sound. Balanced, full of mojo and just wonderful. What is the oposite of a one trick pony? A mule. Seriously, this handles the most old school sounds and can even be pushed to do metal with a cool attitude. It should have all you ever want and more.
The Mothers Milk also is just a gloriously classic single coil. It is woody and snappy, can sing like nobodys buissiness and so on. The Irish Tour and Slowhand are actually based on it, they mostly just add more power and mids to the design, so around half the single coil range is actually a variation on this design, it is that good.
The two also work together really well and should give you a an insanely versatile old school set of pickups that shoot character and mojo around like there is no tomorrow.
Cheers!