Most of the metadata you should be worried about resides in 2 places:
- Document Properties:
You can just delete/remove those from that windows. Also, there's the "Additional Metadata" button, that mostly includes information such as which software was used, possibly editing time, authors etc. Go ahead and remove those too.
- File Properties when you "right click" on the file and click on "Properties" and then "Details" (assuming you are using Windows). There is an option to have the metadata removed.
Since you mention Adobe Acrobat in particular, there are 2 options to have the software do the clean-up for you. I am attaching a capture from an older version, but it shouldn't be much different in newer versions.
The "Sanitize Document" just goes ahead and removed everything (even hidden text). The "Remove Hidden Information" analyzes the document and lets you choose what to remove. There is a catch though. In some case, if on the same page exist both images and text, the whole page is flattenned and converted into an image, along with some quality loss.