Can the desire "to become perfect," to grow in holiness, be one's motivation for being ordained a priest? On first consideration, this might seem totally inappropriate, as the priesthood is not given in the first place for a man's personal perfection, but in order for him to serve Christ, as his representative. Thus, St. Alphonsus Ligouri, while he describes the right motivation for religious life as "to bind oneself more closely to God, or to correct the transgressions of one's past life, or to fly from the dangers of the world," describes the right motivation that is a sign of a vocation to the priesthood differently, saying that one should desire "to serve God, to spread his glory and to save souls."
This difference between religious life and priesthood, namely that religious life is directly ordered to a personal and real conformity with Christ, to perfection in love of Christ, and thereby to the service of the community and building up the Church in love, while the priesthood is directly ordered to a sacramental and representative conformity to Christ, to the service of the community in Christ's name, is a real difference, and does imply that one's motivation for the priesthood in a certain sense cannot be primarily for one's personal perfection in the Christian life.
However, this sharp division (personal perfection in Christian life, service of the Church, etc.) is not the concrete way in which a vocation is usually experienced. The Apostles did not know in all specificity what they were being called to when Christ said, "Come, follow me." They were attracted by his person or inspired by his mission, and they followed him both to be with him and to accompany him on his mission. In most cases, a person perceiving a vocation cannot define his motivation to embrace that way of life in terms of a very precise single goal. He chooses the way of life as a whole, with all that is included in it.
Now, is a special call to perfection included in the priesthood? It is. John Paul II, in Pastores Dabo Vobis, says that priests "are called not only because they have been baptized, but also and specifically because they are priests, that is, under a new title and in new and different ways deriving from the sacrament of holy orders" (n. 19). And Vatican II says, "Since every priest in his own way represents the person of Christ himself, he is endowed with a special grace. By this grace the priest, through his service of the people committed to his care and all the People of God, is able the better to pursue the perfection of Christ, whose place he takes" (Presbyterorum Ordinis, n. 12). The awareness of this special calling and grace, often concretized by experience of holy priests, can be included in the discernment and decision to offer oneself for the priesthood, to seek ordination. Whatever the special aspects of priestly life that initially attract one to it, what is essential is that it be embraced in its totality. E.g., one person might, prior to any thought of the priesthood, be drawn to celibacy, to devote his life to the things of God, and through this desire come to desire the priesthood in particular. Another person might not at first be particularly drawn to celibacy, and first find his vocation to it in his desire to serve others in the ministerial priesthood, which in the Roman Rite is connected with celibacy. (In this latter case it is nonetheless important that he come to appreciate the proper value of celibacy and to embrace it freely, and not only as a extra obligation he has to submit to in order to be a priest. But that's matter for another post.) Similarly, the "path to perfection" of the priesthood might be for one person an important aspect of his initial aspect desire for it, while for another person it is not, and only in his desire for and commitment to living a good priestly life that he sees in that way of life his path to perfection.