Hi
Do you know what is on each disc? (I don't know what comes with the starter pack but I assume base game on disc 1 and expansions on disc 2)
I would suggest first cleanly uninstalling whatever files are already there using this guide: When you uninstall TS3 games on your Mac using the uninstaller, the game leaves behind stray files and isn't completely removed from your computer. These files may conflict with future installations. It is best to completely remove them. BluebellFlora's website provides a guide on how to do this:
http://bluebellflora.com/the-sims-3-on-a-mac/how-to-do-a-clean-uninstall-and-reinstall-on-a-mac/
After cleanly uninstalling, install the base game and patch it up to date. If you cannot update via the Launcher, download and apply the latest cumulative manual patch (called the superpatch) for Mac.
Check that your game works properly at this point and then try adding expansions (if that is what is on disc 2).
Caspin