I like the free trial option, without ever entering any credit card info. A free trial gets the user used to what they are getting, and you don't have to upsell them later. If you just let them use the free version from the start it is easy for the user to end up thinking "oh these ads on the side aren't too bad" or "oh I don't need to have my company logo at the top" etc etc - so it is more difficult to get them to convert. Once they have used the version with there logo and no ads (or whatever it is you are offering) it is less likely they will accept downgrading.

The other issue with a free trial is it gives you thirty days of your product being out there before you need to get the billing working. Maybe you can launch next week instead of next month.

The other thing I like, that is rare to see (and would probably suit your time tracking app), is a working demo. Allow people to use the app without having to create an account or enter an email etc, just have some dummy data and preferably ensure the data is cleaned after each use (to prevent someone entering objectionable material). Most people that are likely to use your app are smart enough to go and click around and see if it is what they want. Then they can sign up to a free trial and you have a customer who is more likely to turn into a real customer.

Good luck.