I guess it would be a bit out of context to ask WHAT to test in this forum. Basically you need to learn what it takes to be a good tester. Tools like Ranorex might be able to help you but they are just tools they are not testing. Automation or Checking is really just a subset of testing. Determining what to test is what professional software testers do.
For some light reading you can take a look at the heuristic test strategy model
http://www.satisfice.com/tools/htsm.pdf. This might give you some ideas on what you could be testing.
To be a good tester, you need to learn how to do that. As a start, I would recommend Cem Kaner's black box testing series.
http://www.testingeducation.org/BBST/ or take the course from the Association for Software Testing AST. If you ever have a chance, take the Rapid Software Testing by James Bach/Michael Bolton. It's excellent. Attend conferences and start reading the blogs of respected testers like
http://www.developsense.com/blog/ or
http://www.satisfice.com/blog/ and follow on twitter.
To answer your specific questions, I am sure the idea of your application came from somewhere. If there are no requirements at all then you are left to your own devices to develop some good testing scenarios. Try this for a read ...
http://www.kaner.com/pdfs/ScenarioIntroVer4.pdf. But if it is something like eCommerce, there are some obvious scenarios. Browsing flow, Buying flow, Checkout flow etc. ECommerce is not a new area and you can take a look at other things that already exist out the big wide world too. You can get ideas from similar software too. Try
https://cwiki.apache.org/confluence/dis ... E-commerce to see some example ideas.
In short....
1. Learn how to be a good tester.
2. Continue learning.
3. Use tools wisely (like Ranorex).
4. Rinse and Repeat.
I also can't end this post without asking. Why 3?