-
It's a bit pricey (though much cheaper than a teacher, not sure on the relative effectiveness though), but I found Melodics to be super useful in terms of getting the actual mechanics of independently coordinating your fingers to play what you see on screen. Then moved over to FlowKey which is more focussed on teaching actual music and has quite a bunch of classical to get you going. I imagine once you're relatively proficient with that you should be in a position to just grab sheet music and work away. Naturally you'll need to get up to scratch on your sight reading too, but I've found this just to come naturally with no real explicit practice.
The main thing I've found is to do it as often as possible, even if it's just 5-10 mins a day. It makes such a difference vs 1 hour once per week or something like that.
Granted, I'm not really coming at it from a playing classical piano stuff, and more from a music production point of view. If you're looking to use either Flowkey or Melodics (or any of the other host of similar services), you'll need a MIDI keyboard. Whether just a standalone MIDI controller or a MIDI-capable electronic keyboard.
How hard is it to learn the piano? Am imagining an electronic keyboard with headphones so I don't annoy the neighbours. I had lessons when I was 8 but didn't get far because I disliked the teacher and never did any of the practice sessions I was meant to. I would like to play classical stuff, not just the plinky plunk things you have to do when you're learning.