Websites to track down relatives by your birth certificate?

[2QUIK6]

I have a need to track back who my great great grandmother was but none of our family trees go back on my Grandmothers parents side.
And I don't know if she was on my grandmothers father or mothers side.
This was from my Dad's side of the family, which unfortunately, there's not many relatives on that side still alive for me to find out.

I've heard that it can be done using my birth certificate, which lists my father and his birth date/place.
Then from my Fathers birth cert, locate my grandmothers birth cert which will list her parents birth date/place.
Then from that locate my great grand parents bith date/place,
And then finally locate my great great grand parents.

I have the persons name and State in which she was born, but thats it.

I know there's websites that can retreive birth certificate info if you have the persons name and birth place, but how good are these sites...

Has anyone used one that was worth the $$ you have to pay?