My opinion is that there is no such thing as a best way to learn ANY piece, there is a best way for each specific difficult section.
I believe that there are rules we follow no matter what level or piece we are learning or our own level for that matter. One of the most important constants to our practice is; when you practice it is INEFFICIENT to practice with uncontrolled pausing. The definition of uncontrolled pausing is, when one plays and then must stop (because of many different unsolved problems), interupting the constant tempo of the piece.
If you can play, by memory, a phrase of music, finger perfect, note perfect and at a percentage of the normal tempo (even 1% would work but it is very hard to play and/or sense playing evenly at this speed), you have set up the basis for gaining mastery over what you specifically practice. From slow and controlled comes control for any speed.
If you can play something at say quater tempo completely controlled and with near 0% error rate, then pushing up the tempo becomes automatic and not an effort. I disgaree with slowly notching up the tempo because this is missing the point of controlled playing. If you can play controlled you can play any tempo, as simple as that, there are not say 20 steps to take, notching up the tempo a little bit every day, very inefficient even though it will work.
Some people believe that to play fast you must practice fast, this is incorrect, also it is wrong to think that to play big loud sounds you have to pound on the piano. Everything with our hands centres in on comfort, effortlessness and control, of course all of these are commanded by the sound production but that is another issue. If you can play completely controlled you can play fast. Still I have met many people who have played piano for many years and do not know what controlled actually means. Identifying something playing controlled actually takes a lot of experience knowing what it means to play controlled. And one person might play controlled slightly different to the other, this is where experience from teaching many different hands can help, but really you only need to know your own hand and konw what it means to play controlled. However you will get ideas of control by observing masters play and try to put these elements into your own playing. Talking about what it means to play controlled can open a whole new book of discussion.
When we practice we aim to get the notes memorised and comfortable to play. Then alterations to the sound can be more easily achieved. We need a strong foundation of control and accuracy before we can decorate up our music and make it sound nice. Also we need to undertsand how phrases can be played with one movement of the hand, yes there are many movements in the hand but we must strive to see many movements as one whole movement of our hand. This is developing your muscular memory, making combinations of movements feel like one movement.
We can only ever achieve this muscular memory if we practice WITHOUT uncontrolled pausing. I am yet to see anyone not play a phrase of music at tempo after demonstrating to me they can play it half tempo note perfect, finger perfect, completely controlled with close to no chance of errors. I do however see people struggle through phrases of music that they are practicing with uncontrolled pausing. This uncontrolled pausing can be as obvious as completely stopping, or as subtle as a rushed movement to a new position.
And Metronomes, they should all be burnt or kept away with a very long stick. I believe they are a useless device for keeping you in time, you should have an inbuilt timing device in your head. You must know what it means to play evenly without a machine telling you so. It is a security blanket, and also music doesn't really walk well on the tightrope set by metronome perfect tempo.