What to do?

Hello folks, it's your correspondent from Down Under again. Really looking forward to a week in NYC in mid-January and to seeing both Hugh Jackman and Bradley Cooper in their respective plays. So now I want to book a couple of musicals. Now please understand that I really don't know the way things work so I would be grateful if you wouldn't dismiss this post as dumb (as someone did regarding my previous question about a show possibly being extended!)
Anyway, I see that I can get tickets for On The Town already - but should I? Or should I wait until the reviews are out? Your advice would be appreciated.
I also see that some shows have tickets for sale through to January but January 4 seems to be the magic end date. What's up with that?
Is Hedwig likely to go beyond October even without a recognized star?
I know I can tickets for Wicked, Phantom etc but we get that sort of show down here so they're not really under consideration.
I'm hoping for a revival and something new.

Thanks guys - really appreciate your help.

Thanks dramamama611, that's helpful. I guess the message is, be patient. And thanks for the recommendations.