In general, it's okay to let noting happen by itself... but if it gets too speedy or compulsive or neurotic or out of control it's okay to note "thinking, thinking" and take a few deep breaths to relax and regain some equanimity.
By the way, if you want to know the secret to becoming an advanced meditator, I'll tell you it: whenever there is a question about should I do X or should I do Y, the very best answer is "do X for a few sits and see what happens, then to Y for a few sits and see what happens, then decide for yourself. If you can't decide, then describe the results of your experiment and ask advice. That way you'll know directly what works best for you and/or get the best possible information from others to guide your practice."
I'm being a little silly here, but honestly if you study people who get very good at meditation, you'll see that they do these little experiments all the time. They don't try to "figure out" the right answer ahead of time. Instead they actually run a few experiments and then the answer that works best for them becomes more obvious.
