Are you trying to display the whole PDF in a WordPress Window? If so I can't help.
I have several PDF files on my site. For some I just have a bit of text with say "Safe boating handout PDF" then a sentence for description. Click on the link and you get the whole PDF file to download and save or view.
I have some with thumbnails of an area marine chart and the thumbnail is mapped to the PDF file, descriptive text is next to the graphic that describes the area of the chart, click on the thumbnail or text link and you get the PDF file.
Yet others have a thumbnail of a poster - click on the poster and you get a larger image so you can see a larger view of the Poster to tell if the Poster is the one you want, then click on a link next to the original thumbnail for a PDF of the Poster.
Three versions - hope this helps a bit.
If you want to see what I did live - you should be able to click on my name and go to my site - some of the examples are in the standard Posts and the rest in "PE / PA Help"
Easiest? - probably just some large text "Read the latest newsletter" or what ever and the text is a link to retrieve the PDF file. Or a small graphic that links to the latest PDF newsletter. NO need for any fancy Plug-ins unless you want to get fancy.
Some like to put a short summery or headlines of what is in the Newsletter to get visitors interested in reading the Newsletter. Make your visitors WANT to click on Read the News.