Welcome to rootschat Jodi.
I have no experience with USA research, but generally it is advisable to purchase your great grandmother's birth certificate in the hope that that will give her parent's names. Then you can look for their marriage and births.
I don't understand your time line (greats and great greats etc), but when you find your ancestors who were born in Scotland, you will need the website called Scotland's People:
http://www.scotlandspeople.gov.uk/You have to sign up and purchase credits to view records.
The IGI is also worth looking at for Scottish records:
https://familysearch.org/search/collection/list#page=1®ion=UNITED_KINGDOM_IRELANDScroll down the page to S for Scotland.
If you would like to give us some names, places and dates then someone may be able to give you some help.
Your search obviously starts in the USA then will later move to Scotland, so you may need to start a new thread later. (don't do that yet - wait to see what responses you get here first).