The norm is that if a man feels called BOTH to the priesthood and to a particular religious order, he would enter the religious order with the intention of becoming an ordained religious. In many clerical orders (such as the Carmelites or Dominicans) this is normal, as most members are priests. In other groups, the superiors may have the man enter the order first, and then the superiors would discern whether the man is called to be a priest as well, or a lay brother (I know some Franciscans do this, as well as certain monastic orders.)
So, it really depends. If one is drawn to a religious order where he could be a priest, or if he is so drawn to a particular order that he wouldn’t mind if it was decided he was to be a non-ordained brother, he would enter religious life first. If the call to priesthood is so strong that he would not feel called to an order that would not have him ordained a priest, he would discern being a diocesan priest, or a member of another order.
It is also possible that one may be ordained a priest within a diocese, and later discern that he is called to religious life, and so join that order as an already-ordained priest. This can’t be something that a man plans, of course (be ordained in a diocese first, then once one is a priest, plan to join an order) but a progressive discernment that leads one closer to Christ by later becoming a religious.
If you had a question like this for a particular order (what are the chances I could be a priest and member of this order? Could the superiors change their minds about my priestly calling later on? etc.) the best person to ask would be the vocation director for that particular order.
Hope this helps!
In Christ through Mary,
Frank