Answer

There are several paths to learning how to play the piano.  I cannot say that one is clearly better than the others, as I have not taken all of the paths.  Different doesn't necessarily mean wrong, it just means different.
 
Whichever path you take depends upon one's goals.  Do you want to just play for your own personal enjoyment?  Join a band?  Wind up at Carnegie Hall?  Just noodle around, every once in a while?  Be able to play by ear?  Play for family and friends at get-togethers?

As you ask about programs and websites, I think it worth noting that people have been learning to play the piano for the past 350 years without any such aids.  Clearly, history has proven they are not an integral part of learning.  Can they be a part of it?  Most certainly.
 
With that said, my path has been mostly a traditional one.  I took lessons from a piano teacher, learned sight reading from day one, spent very little time on memorization, a fair amount of time on technical exercises, focused on 'method books' in the early years, and incorporated music theory.   I intentionally did not favor one genre over another, as I wanted to take a well-balanced approach to learning the instrument.  I played classical, pop, broadway and jazz, as I selected supplemental materials to the core method books that were selected for me.
 
In terms of a practice routine, daily practice is essential, if you wish to progress in any significant way.  Most piano teachers recommend at least 30 to 60 minutes per day.  If you have piano lessons once a week and are expect to perform last week's assignment at a lesson, you cannot cram in 4 hours of practice in the morning of the lesson and expect to do well.  I've tried it before.  The brain requires time (some even say 'sleep') to digest concepts.

Technical exercises, practiced daily, will greatly help you develop finger control, allow you to execute runs and scales smoothly and improve dynamics.  Even if you practice it for five to ten minutes, those are baby steps in the right direction.  The problem with these technical exercises is that they are not fun and really more like work. Much like how professional football players take laps and lift weights.  However, they are important to building a good foundation, which will be necessary as your piano studies advance in complexity.

Sight reading was one of my personal goals when I first started the piano.  I wanted to be able to pick up 'any' piece of music and just play.  It is a skill that takes a very long time to develop, very similar to regular reading.  You start off learning ABC and many, many years later, you are able to read the works of Shakespeare.  Like technical exercises, this is work -- make no mistake and must be practiced daily to achieve proficiency.  Some additional thoughts on sight reading can be found here.

Garrick Saito's answer to How can I improve at sight-reading on the piano? How long should I study new music before I move on? How difficult should it be relative to what I can play with practice? Are there certain sets of exercises or pieces that are good to use?

Garrick Saito's answer to What are tips for improving my ability to sightread music on the piano?

Garrick Saito's answer to How can I improve piano proprioception?

No matter where you are in your piano studies, you will come across one particular  spot in the music that is more difficult than the rest.  Part of my practice is to spend extra time getting over these hurdles.  A lot of people seem to just blast past them, inevitably playing these difficult passages incorrectly or sloppily.  Here are some thoughts on getting through difficult areas.

Garrick Saito's answer to What are some ways to deal with anger or frustration at a technically difficult passage of music when practicing piano?

Once you have the notes down on any given piece, you'll want to spend some time focusing on dynamics, paying extra careful attention to music notation; crescendos, loudness, staccato, fermatas, pedaling, tempo and so forth.  Practice and just let your mind go.  Feel the music and bring your own emotion and interpretation to the piece, rather than to robotically plunk out the notes.  This is where the beauty in music comes from.

Everybody has their own practice routine, which may differ from person to person.  I'm hesitant to say that there is any one 'right' way.  However, daily practice is essential, if your goal is progress quickly.