I confess copying a topic from PrayTell. I have never had good fruitfulness with the effort of gathering liturgical ministers before Mass.
In one parish, I had to actively discourage it, as one priest liked to have “wrestling matches” with the older servers, and another regular visitor used to ask servers to help him get his cincture tight by pressing on his belly. Enough said?
In my current parish, we have no servers. The priests greet parishioners before Mass as well as after. Only one lector is in the opening procession, and we only use extended processions during Advent, Christmas, Lent, and Easter.
I like the idea in principle. Our music groups pray after warm-ups, usually about 10-15 minutes before Mass. One of my directors has a long-standing tradition that after the prayer, the members offer peace to one another. Then, at the sign of peace, they all move into the assembly and exchange peace there. I like that tradition.
How would you pray before Mass, if you would institute it in your community? Who would be included?
Catholic Sensibility 
Wow, we pray at my parish, asking God to give us the grace to worship Him reverently and serve the assembled Eucharistic assembly properly. Using prayer time as a cover for perversion: is there no lower limit for human depravity?
We always have the rosary before Mass, this parish has done that as far back as anyone can remember. We also have a prayer after the final hymn, “O Sacrament most holy, O Sacrament divine, all praise and all thanksgiving be every moment thine (repeated 3 times). Praised be Jesus Christ, now and forever, Amen.” I didn’t grow up here, so I don’t know if that is a Franciscan thing, but apparently the Franciscan nuns who used to be here impressed upon everyone that you did not leave until that prayer was said. Visiting priests always comment that it is nice not to be run over on the way out.
The choir which I am a member of always says a prayer before warm-up.