You will want to complete as many of the lower division courses for your major as you can before transfer. An example of Modesto Junior College to UCB and UCSD for the political science major:
http://web2.assist.org/web-assist/report.do?agreement=aa&reportPath=REPORT_2&reportScript=Rep2.pl&event=19&dir=1&sia=MODESTO&ria=UCB&ia=MODESTO&oia=UCB&aay=14-15&ay=15-16&dora=POL+SCI
http://web2.assist.org/web-assist/report.do?agreement=aa&reportPath=REPORT_2&reportScript=Rep2.pl&event=19&dir=1&sia=MODESTO&ria=UCSD&ia=MODESTO&oia=UCSD&aay=14-15&ay=15-16&dora=POLI+SCI-INTER+REL
You can use http://www.assist.org to look up listings for other UCs and CSUs and other majors.
Completion of IGETC before transfer (as certified by your CC) will be accepted for completion of general education requirements at most UCs and CSUs (note that UCSD has different residential colleges with different general education requirements; not all of them accept IGETC as fulfilling all such requirements). IGETC is not required for admission, but if you do not complete it before transfer, you will need to complete the campus’ general education requirements after transfer if you have any additional needed courses.
For the private schools, look up their lower division requirements for your major and their general education requirements to see what you can take at CCs that is likely to cover those requirements.