Hai:

I need some advice on this. I get confused with dumpcycles, etc.

I need one full backup on the 1st day of every month. And then from sunday
to saturday through the entire month, I need to take incremental 
backup. How do I take it? I mean incremental backup from the 1st day of
every month to the last day of the month.

Or essentially, like the towers of hanoi:

sun mon tue wed thu fri sat sun
0   3   2   5   4   7   6   9/1

Is it feasible to take it this way?

Else, suggest some decent solution for my backups.

Regards,
Nitesh