PDFs have changed a lot over the years, so it is very important you use the correct settings. As standard (or profile) we recommend you to use PDF/X1a:2001 and as compatibility Acrobat 4 (PDF 1.3).
Note: do not forget to convert your text to outlines
Below, you see the "save" screen of Adobe Illustrator. On the image we marked the fields that relate to these settings.
In Figure 2 we see the "export" screen of Adobe InDesign. On the image we marked the fields that relate to these settings.