Tldr: There are four “main” Eucharistic Prayers, plus those for Reconciliation and for use in Masses for Various Needs, each bringing its own beauty to the mass as well as diversity and variety to the liturgy.
EP I - is the “canon of the mass” and, before 1970, was the only Eucharistic Prayer. It is still the preeminent Prayer but is also the most involved in terms of its gestures and language as well as its lengthy lists of saints (which, while historically interesting, do tend to go on a bit…). Some priests seem to be almost allergic to it.
EP II - a shortened version of the Roman Canon with parts included from the Hippolytus’ Apostolic Tradition. It’s the most common partly because it’s the shortest (some people have these things called jobs) but also because it comes with it’s own built-in, yet detachable preface (the part immediately before the Eucharistic Prayer), making it useful year-round.
EP III - tends to be a popular choice for those looking for an alternative to EPII - especially on Sundays. Like EPII, there’s an optional extra commemoration of the dead.
EPIV is probably the rarest of the four main Prayers. While its use of masculine pronouns (and length) probably has something to do with this, the main reason it’s used so infrequently is because it has it’s own preface which, along with the prayer itself, forms a single complete unit. This means that it can’t be used at any masses with their own proper preface: pretty much anytime except Sundays and weekdays in Ordinary Time.
Next are two Eucharistic Prayers for Reconciliation which “may be used in masses in which the mystery of reconciliation is conveyed to the faithful in a special way”. The rubrics suggest examples from amongst the masses for Various Needs and Occasions and Votive Masses, as well as masses during Lent of course. These Prayers can be used either with their own preface or with other prefaces referring to penance and conversion, e.g. prefaces for Lent.
Finally there are four Eucharistic Prayers for Use in Masses for Various Needs:
- The Church on the Path to Unity
- God Guides His Church along the Way of Salvation
- Jesus Who Went About Doing Good (nice prayer, shame about the title)
The rubrics provide some suggestions for when these might be used but sometimes these prayers might be particularly appropriate in light of the readings of the day. These prayers also come with their own built-in but detachable prefaces.
Ideally, priests should reflect on the readings/theme of the mass and find a Eucharistic Prayer which resonates with it or at least give some thought as to which Eucharistic Prayer might be appropriate.