how can i save PDF for printing properly? what are the general and compression right way of saving?

Adobe recommends use of the PDF/X-4 presets, not the Press Quality presets which were designed for 1990's style print workflows. If you print the PDF from Acrobat or Reader to a PostScript or other non-PDF direct printer, this will yield best results. And if your PDF file is directly submitted to a native PDF printer, virtually all such printers will do a better job printing from PDF/X-4 than either PDF/X-1a or PDF produced with the ​Press Quality ​settings.

          - Dov