I took lessons. From Grade 1 to grade 8. You need to practice almost every day, so yeah you'll need your own piano, or at least a big, piano-size keyboard at first. Like Rye said, you'll need a piano at some point, as there's a tremendous difference between even the best keyboards and an actual piano.

Chances are, you won't spend too much time learning modern music. You will learn some, but not a lot. Instead, for the most part it'll be simple tunes like Twinkle, Twinkle Little Star at first, and Sonatinas other classical music as you get more advanced, and other music that allows you to see the theory you've learned applied in music composition. And yes, you'll learn lots of theory. At least, that's what I was taught. I got sick of it after 7 years, and picked up the guitar. Although it wouldn't surprise me if I got back into the piano again, sometime down the road.