For letter with ^ = option + i and letter
For letter with ~ = option + n and letter
For letter with ' = option + e and letter
For letter with ` = option + ` and letter
For letter ç = option + c
But if you want to do different, go to System Preferences/Language and then select Text/Input sources, after check the box for US International PC. If you don't use multiple keyboard, delete the others keyboard from list and clear the box for Show Input Menu in Menu Bar.
Voalá, you ready to use! :))