Content types are missing I'm working with a drupal 7.50 installation on a local host. 

My problem is that the basic content types are missing from my site. My custom content type is still visible and usable.

So far, I have checked under all menus to see if they've moved or been disabled, but I don't even see them. I've also tried clearing my cache, which didn't fix it. 

Some of the modules I have enabled are drupal commerce, display suite, panels, and search api. 

Any help would be much appreciated.
It seems like you are running a Drupal that was installed with the minimal profile. That profile does not create the Article and Basic Page content types. So, they are simply not there, clearing the cache will not help.

In order to get the content-types back you need to either:

a) Create them manually
b) Use the parts of the standard_install() function from profiles/standard/standard.install file that are additional to the minimal_install() function from profiles/minimal/minimal.install file to add the missing configuration. Kind of tricky, but not too much code there all in all.
c) Use the Features module to transfer the configuration of the content-types you are missing from another site installed using the standard profile.

N.B.: You know that already, but still, you should keep backups all the time, this may need a couple of try-n-error runs.

Good luck!