What is a good ratio of "What I want to research" vs. "My experience that shows I can research" in a Statement of purpose?
A Statement of Purpose isn't a money-back contract stating exactly what you're going to do.  It's okay if you end up doing something different from what you imagine and write about in your admission essay.

Background information about yourself should be included as needed, so the reader can understand your account of what has been especially meaningful to you so far, and your personal motivation to go to the next level with your studies.  You don't need to write a complete catalog of everything you've done.  But do include relevant bits so that your essay hangs together as a projective story.

The admission essay is a place where you can show some inspiration.