There is a separate App store for Mac Applications.
If you are seeing Apps for iDevices, you may not be using the correct access method. From your Mac, use the 'App Store' App.
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Unless your needs are very unusual. Preview works fine for most ordinary uses. Personally I find Acrobat Reader awkward and difficult to use. I much prefer Preview.
Web site software often warns you that you may not be able to open things, then when you ignore their advice the files open directly in your Web Browser using Preview, or can be sent to your download folder and open in preview when double-clicked.