You are so right Pep! It must be something that you are really enthused about, you don't want to spend 3+ years researching a topic that does not inspire and motivate you.
Personally, I had applied many different places and was actually offered two different projects. I chose what I thought was the most interesting... and it wasn't what I had originally considered ! But as Ann says, pick wisely !
I agree especially with Pep! Find something you like and see where it takes you! Keep an open mind and see what new twist you can bring to the topic! It maynot be something you had even thought about!