How can I update query to use GROUP BY instead of DISTINCT while still preserving ORDER BY?

Question

Trying to make this query more performant (basically I need to have distinct speech_ids from the speech_candidate table while at the same time counting the number of duplicate speech_ids for each of the unique rows from the speech_candidate table we're pulling):

SELECT
  * 
FROM 
  (
    SELECT DISTINCT ON (speech_candidate.speech_id) 
       speech_candidate.speech_id
     ,(speechtype_id = 7) AS is_position_paper
     ,(speechdate IS NULL) AS is_null_date
     ,(
        SELECT 
          COALESCE(shorttitle, '') 
        FROM 
          office oc 
        JOIN 
          office_candidate oc2 USING (office_id) 
        WHERE 
          oc2.candidate_id = candidate.candidate_id 
            AND officecandidatestatus_id = 1 
        ORDER BY 
          rank 
        LIMIT 1
      ) AS shorttitle
     ,speech_candidate.speech_candidate_id
     ,speech_candidate.speech_id
     ,speech_candidate.candidate_id
     ,speech.speech_id
     ,speech.title
     ,speech.speechdate
     ,speech.location
     ,speech.key
     ,speech.quote
     ,candidate.candidate_id
     ,candidate.firstname
     ,candidate.middlename
     ,candidate.lastname
     ,candidate.nickname 
    FROM 
      speech_candidate 
    INNER JOIN 
      candidate 
        ON speech_candidate.candidate_id = candidate.candidate_id
    INNER JOIN 
      office_candidate 
        ON candidate.candidate_id = office_candidate.candidate_id
    INNER JOIN 
      office 
        ON office_candidate.office_id = office.office_id
    INNER JOIN 
      speech 
        ON speech_candidate.speech_id = speech.speech_id 
    WHERE
      office_candidate.state_id IN ('NA', 'AL', 'AK', 'AS', 'AZ', 'AR', 'CA', 'CO', 'CT', 'DE', 'DC', 'FL', 'GA', 'GU', 'HI', 'ID', 'IL', 'IN', 'IA', 'KS', 'KY', 'LA', 'ME', 'MD', 'MA', 'MI', 'MN', 'MS', 'MO', 'MT', 'NC', 'ND', 'MP', 'NE', 'NV', 'NH', 'NJ', 'NM', 'NY', 'OH', 'OK', 'OR', 'PA', 'PR', 'RI', 'SC', 'SD', 'TN', 'TX', 'UT', 'VI', 'VA', 'VT', 'WA', 'WI', 'WV', 'WY') 
        AND office_candidate.officecandidatestatus_id = 1 
        AND office.officetype_id = 'C' 
        AND speech.release_id >= 1 
    ORDER BY 
      speech_candidate.speech_id
     ,is_position_paper
     ,is_null_date
     ,speech.speechdate
  ) sc 
ORDER BY 
  sc.is_position_paper
 ,sc.is_null_date
 ,sc.speechdate DESC 
LIMIT 50 OFFSET 0

Would it be better to do this via GROUP BY or is DISTINCT really what I want to use here? Again, I need to both dedupe AND add a column with a counting of the duplicates for each row.