You should try to find a used digital piano, not an electronic keyboard. With your budget, you should be able to find a decent used digital.
Why do you want to play the piano? What music do you want to play? Pop? Classical? Jazz?
The answer to this will shape the direction of your musical learning experience. You can learn music theory (how to read the stave, key signatures, etc.) from books for any style of music. Start there. It's cheaper than a teacher but will take more time.
If you start with improvisation, you'll be able to play something very quickly and you'll develop a skill that isn't taught to most classical music students.