Commentaries usually describe the criteria of 1st jhana only in term of 5 jhana factors. IMO, there are two important points(criteria) from the main Nikayas that seemed to have been forgotten, rarely or even never mentioned/discussed by Buddhist monks/teachers. Those two criteria are:
1) kāmasaññā ceases, as mentioned in Anupubbanirodha Sutta (AN 9.31) http://www.accesstoinsight.org/tipitaka ... .than.html
It depends on the translation of kāmasaññā. I believe it means kāma-based perception.
2) vācā ceases, as mentioned in Rahogata Sutta (SN 36.11) www.accesstoinsight.org/tipitaka/sn/sn3 ... .than.html
vācā means speech (verbal fabrication)