First of criteria fit for message (5)
I believe the answer is:
cable
'message' is the definition.
(cable is a kind of message)
'first of criteria fit' is the wordplay.
'first of' indicates taking the first letters.
'fit' becomes 'able' ('able' can be similar in meaning to 'fit'**).
The initial letter of 'criteria' is 'c'.
'c'+'able'='CABLE'
'for' is the link.
(Other definitions for cable that I've seen before include "Strong line" , "Telegram; thick rope" , "Naut. length; transmit" , "Communication - wire - 200 yards in length" , "A message transmitted" .)