I have gone through a number posts on stackoverflow and numerous articles about Unit Tests. I am just trying to figure out that what I have understood is right.
I'm not unit-testing anything, because instead I want the integration and/or system tests to:
For details, see Should one test internal implementation, or only test public behaviour?
Reversing your question, I suggest that the only code which you should unit test is code:
a) Which isn't going to be tested at all by integration and/or system testing (and if not, why not?)
b) Or which should, for whatever reason, be tested before integration/system testing (perhaps because of how which your project's development is partitioned to several developers in parallel)