I think your plan is great. You'd pay $20/hr for piano lessons, you could buy a good instruction book for every hour of lessons you skip. And youtube is a great resource which I'm using for guitar instructions right now.

I learned piano as a kid and hated it. I took it up again as a teen and retaught myself and loved it. When I went to college I learned to play guitar (self-taught) and when I later took up piano again I could use ideas of chord structures and keys to play piano like it was a guitar, with the result being an explosion in my ability to compose on piano.

I had a Roland KR-375 digital piano for many years -- just awesome, better than a stringed piano. But it was over $2000. Two weeks ago I bought a Casio PX-130, used but essentially new, for about $250, half the list price. I'm stunned at how good this piano sounds and feels. Even at full price it would be a great deal. I can also plug the usb into my mac and it functions flawlessly with garage band. I'd highly recommend scouring Craigslist for a digital piano. When you find one in your price range, google some reviews and see what people say about it. Do not buy a keyboard that does not have weighted keys -- feel is extremely important with a piano

Good luck! Piano and guitar are really the best two instruments in my book.