Any man seriously considering a vocation to the priesthood should have an interest in canon law and the liturgy, since they will rule most of his life. Therefore, they tend to be part of the general charism of the priesthood rather than the particular charism of different religious institutes. As others have noted, for diocesan priests, one’s bishop determines whether or not one studies canon law. Most large religious orders also contain a few canon lawyers; in this case, the religious superior decides whether or not a man will pursue higher studies in canon law. The Jesuits and Sulpicians have long traditions of teaching in seminaries and therefore contain a good number of canon lawyers.
Now for your other interest, the liturgy: most monastic orders (the Carthusians being a debatable exception) have an interest in the liturgy, since praying the Liturgy of the Hours and celebrating the Mass are the principle elements of their lives. Among the Benedictines, the Solesmes (French) congregation is quite interested in the extraordinary form of the Roman liturgy and the monasteries of the English congregation tend to favor the “new liturgical movement.” The Swiss-American congregation has long been a bastion of the original liturgical movement, pioneering many of the changes instituted by the Second Vatican Council. However, there is a lot of variation from monastery to monastery.
Canons regular also tend to be very interested in the liturgy since they live together and pray together. You might want to look at the Canons Regular of St. Augustine and the Premonstratensians/Norbertines (particularly St. Michael’s Abbey in California). Finally, the Dominicans are a very liturgical order and are also known for their commitment to study. They still pray together and, like the Premonstratensians, Carthusians, Carmelites, and Cistercians, once had their own rite for the Mass (which is being revived in some provinces).
Finally, neither is technically an order, but the Canons Regular of St. John Cantius in Chicago and the Oratorians tend to be interested in the liturgy.
