I took piano lessons for about… hmm… 12 years maybe? Probably from about 6 to 18. All classical trained. As it is now, I cannot improv in the sense that an accomplished jazz musician could. I disagree, however, that a strict formal piano education will somehow leave you improvisationally challenged. I often sit down at the piano and just play whatever comes to me. Some of it is (I think) quite good, much of it is so much noise, but I doubt I could do even that much if I didn’t have some training.
I feel like I can’t stress the importance of a real piano enough. Like somebody else mentioned, an upright won’t take up much more room than an electric keyboard (assuming you leave the electric out and don’t put it under your bed when not in use). I’ve yet to play a single keyboard that gets even close to the feel of a real piano.
Like others have said, it’s the getting your hands to move in very different directions while simultaneously reading music that’s the trick. The first pieces you will learn will most likely have a very repetitive left hand part with a simple melody in the right hand. Sight reading will also take a long time. Until you get the muscle memory of intervals and fingerings for different keys, sight reading will be a very slow process.
Develop your ear as much as possible too. If you hear a tune on TV or on the radio that you like, try to sound out as much of it as you can on the piano for practice. Having a good ear will help you play a piece just as much as memorizing the music.
Good luck! Piano is a wonderful instrument to play. I do it for hours at times. Don’t get discouraged either! Regardless of your natural talent, it’ll be years before you can play what you were probably hearing on the classical channel. But not every popular piece is extremely difficult. You’ll get them all eventually.
And if a six-year-old can learn to read music in a few months of weekly lessons, like I did, you can learn it too.
I have played since I was 10, both jazz and classical. I am bad at cold-reading music, but I can get it in a few readings. I used to be pretty good; nowadays all I am comfortable with is rhythm jazz piano and a few classical chestnuts my fingers still know.
It is a purely mental thing, requiring a coordination that needs tons of practice to work out. Kind of like typing. In fact, I’d say the learning is a little like going from hunt-and-peck typing to fast touch typing without watching your fingers. Add to that that there are large arm movements and wrist movements involved on top of the finger movements, and that you should be able to control the velocity (impact) of each finger on each hand. There are things you can do to help you out, but all in all it takes years of practice.
If you are getting a keyboard, get a weighted key keyboard. A very good option, as Misnomer said, if you are space and money limited, is to rent an electric piano like the Yamaha Clavinova. That’s what I did through college and the first few years of med school until my parents let me take the real piano from home. That’s what my brother-in-law, who has a major in piano performace, does. It lacks something (I find the sound a little “bouncy”), but it is pretty good and more than adequate for learning. Since, like touch typing, it is all dependent on a feedback between your brain and fingers (think of trying to touch type on a flat piece of glass, for instance, it just wouldn’t work), a lot comes back to the weighted keys. I have a non-weighted key Ensoniq keyboard which I find dreadful for any kind of playing for any length of time.
I would highly recommend at least a year of lessons. There is a lot that can go wrong very early in piano playing that will limit your abilities later (if you keep up with it): hand positions, finger positions, the ability to play by ear and by music, reading music, and perhaps most importantly piano music theory. Music theory will help you endlessly later if you decide to take up jazz piano. I was classically trained from 4th to 11th grade, when I joined a jazz band. Since I had some background in theory, someone could tell me that we were doing a I-IV-V or I-VI-IX-V progression in B flat, and to solo using a major pentatonic, and it made sense and became easier to figure out solos and stuff. It helped me play gig sheets, where you are only given chord progressions and you figure out what to do with them.
Good luck. It probably will be quite frustrating at first, as the sounds coming out of any instrument played by a beginner don’t come close to matching what the beginner thinks they should sound like. You won’t be playing Rachmaninoff’s Third for at least a couple of months. But if you wanted easy, take up the Sax-a-boom.
Yes, learn to play the piano! You’ll either get the hang of it or you won’t and if you do you’ll love yourself forever.
I’m self taught and I love to play and write. Sometimes I just close my eyes and make up things and get lost in what I’m doing. It’s a total escape for me.
As for real vs electronic. I have both a Steinway and several electronic keyboards (12 I think). The Steinway is nice but honestly I play my Kurzweil PC88 more. The feel of the action is just like my Steinway, the sounds are very close. In fact, I’ve used the PC88 in many recordings and have had comments from piano players on how much they like the tone of the piano sounds.
But the real reason I like the electronic over the real – headphones and volume. I can sit down and play anytime I want without disrupting the household. Of course the wife never complains when I sit at the Steinway but I bet she would if it was at 2am.
Of course the PC88 is a heavy bastard and you’ll need to invest in a quality stand to use it (and a friend to carry it into the house if it’s still in the box).
I spent a fair amount of time looking at weighted key keyboards and I have not once thought I made the wrong choice with the PC88.
Classical piano training can be geared towards that. But it’s a bad teacher who takes that to be the only possible intention or ambition.
I think that’s not so true when you’re starting as an adult. I played piano as a child, then basically didn’t play much (perhaps once a month or less) for the next 40 years or so. I’ve started again, this year, as an adult taking lessons. I selected a teacher carefully – I don’t need the help with reading music, but I do need help with putting life into the music, and the teacher has been great at that. She picks one piece (usually classical) and I pick one piece (usually jazz or sing-along stuff), so that we’re working on both mechanics and – I don’t know the word, soul? spirit?
The thing about learning to read music is that you can play anything once you have the music. Playing by ear, you have more spontaneity but less range, unless you’ve got an exceptional ear. For me, with minimal musical education or talent, playing from the music is great. I could pick out a melody, perhaps, with one finger, but I couldn’t manage accompaniment, chords (other than standard) or frills.
That’s what I have! 
I absolutely love it, and have often wondered whether I would continue to use it if I were to get an acoustic piano in the house (any acoustic, let alone a Steinway!). I think that I would, if for no other reason than the playing-at-2am thing you mentioned (I have no spouse to bother, but my neighbors might object . . . especially to the Christmas music that I tend to practice year 'round 
).
I’m glad to hear you say that the feel is similar to that of your Steinway: I haven’t played a “real” piano in quite some time, and I sometimes worry that I’ll have a steep readjustment curve when the time comes.
You’re right that it weighs a ton: its non-portable nature is the only thing about it that I wish I could change (I often wish that I could bring it with me to jam sessions). I always have to be very careful when I move it myself, and I kept the original styrofoam pieces that fit on the ends of the keyboard for when I do move it.
Exactly! Well said, both of you.
I doubt you’ll have much of an adjustment time on a piano with good action. An old dead-felt upright thats been stored by a furnace,. perhaps. 
My only real complaint with any electronic keyboard is the lack of resonance when you lay into the keys - the warmth of the sound board and the vibration of the neighbouring strings. But a hint of reverb and it comes close to filling the gap.
I compare it to hanging up a cordless phone in anger. Poking the hang up button with your index finger ble-bloop just isn’t as satisfying as slamming the receiver down on an old proper phone. sklang!
That’s a great analogy!
The other thing I repeatedly notice about my keyboard is where the sound comes from: I have it hooked up to a bookshelf stereo, and the speakers are to my left when I’m sitting at the keyboard. I have a small shelf designed especially for small stereos, but when I tried to put it behind the keyboard (to try and get the sound coming from the same place it would on an upright) it just didn’t work. So I miss feeling like I’m “surrounded” by the sound board – part of that is the warmth and resonance that you mentioned.
I dearly love my Kurzweil, but there really is no substitute for a decent acoustic piano.
I’ve had a Roland elecronic piano with 88 weighted keys for about 12 years now, and I don’t regret it for a minute. It’s (barely) portable, which matters if you move your household goods now and then, it can be hooked up to other MIDI instruments, you can use it with headphones, and you never have to tune it.
I took a few years of lessons as a child, laid off of it due to a skin condition, then essentially started over in high school. I play almost exclusively by ear now, but if you’re someone who like complex music you’ll probably need the lessons… “by ear” can be challenging if the music you’re listening to has complex/unusual chords. For example, I once found the sheet music to Emerson Lake and Palmer’s Tarkus, and spent years struggling through it. It was worth it, though, because I never would have figured out what they were really doing otherwise.
This is all IMHO of course… there are undoubtedly “by ear” players who are talented enough to pick out anything… I’m just not one of them.