I am in the process of applying to graduate schools and wondered what advice graduate students, and really anyone, have about funding for graduate school.

I know there are many public and private sources for support for graduate school, but is it worth it to try to gain support for outside places if you have a variety of programs you are applying to and it might affect your package at some?  Do you think this is an attractive feature for applicants to have?  Or it just complicates things entirely?    

What sources did you wish you had tapped into?  Did you wish you had bargained more than you did?  Can you bargain?  Is that common for math programs?

Any advice would be greatly appreciated.