The P series are serious portable (i.e., luggable) stage pianos, meaning they are used routinely by professional musicians (rock, country, blues, hip-hop, etc.) when they perform. Knowing that they are popular stage pianos made me take pause, because I wanted a keyboard to play classical music.
I tried a lot of keyboards -- mostly Korgs, Rolands, and Yahamas, and now I have a P120 and it's great. Very realistic piano sound sampled multiple times per note from a Yamaha C7 concert grand. Yahama also makes a good effort to imitate the feel of a real piano by graduating the touchweight needed to play notes from heavier in the bass to lighter in the treble, similar to a real piano.
I believe the concert grand piano voice is standard on the entire P line. The P120 has quite a few more bells and whistles, more voices, etc., so compare all features for the whole P line at the Yahama website, decide what you must have and what you can live without.
The keyboards come without accessories, so you'll have to buy a stand (I'd advise a Z stand -- standard stage equipment, which can be adjusted from a basic seated keyboard height to a height where you can play while standing, which some musicians like to do on stage. You'll also need to get 2 pedals if you want both a sustaining pedal and a soft pedal. Also, you'll want a good set of headphones as that's the only way to hear the great piano sound (the on-board speakers are crap), plus it lets you practice in utter privacy!