More help for our priests from the GIRM.
You can always use Eucharistic Prayer I, and you should use it when there is a proper text for the Comunicantes or the Hanc Igitur, or when it is the feast of one of the Apostles, or a saint mentioned in it. Eucharistic Prayer II is only for weekdays. Eucharistic Prayers III and IV are for Sundays only, and IV should only be used when there is no Preface for the particular Mass and on Sundays in Ordinary time.
This summarises paragraph 365.