What Type of Join to Use in this Search?
Probably something along these lines, courtesy of OUTER APPLY:

select 
    --A bunch of stuff
    ISNULL(pic.PImage_Path, 'None') AS PImage_Path
FROM PERSON a 
  LEFT OUTER JOIN COMPANY c
    ON a.Person_Company_ID = c.Company_ID
  OUTER APPLY (
    SELECT TOP 1
      PImage_Path
    FROM PIMAGE 
    WHERE PIMAGE.PImage_Subject_ID = a.Person_ID --Fix this if I'm making the wrong assumption about your key columns.
    ORDER BY ... --Something sensible to determine which picture will be used
  ) pic