I'd definitely go with something like LaunchRock. It will let you set up this page in minutes. You'll want to test your core hypothesis, namely that the value you think the app will provide is actually needed.

As far as how long you wait, I think the general purpose of a landing page like this is to gauge interest. You'll have to drive people to the page somehow. You can do this with ad words and social media relatively cheaply. You'll want to track how many people land on the page, how many people sign up for the waiting list, and how many people engage with you on social media about the app/idea.

You can usually tell pretty quickly if the idea has legs or not. If you are getting some interest and traction, then go ahead and invest in building the app.

I wouldn't worry AT ALL about how long people are on the waiting list. The focus should be determining whether or not there is a market. If you are solving a problem for them, you'll still be solving it in six months when the app launches.