I imagine that first sons rarely went into the priesthood. But what about second sons? Was that common, rare?
Context: anywhere in Europe.
In the 10th and 11th centuries, the centuries when primogeniture-ship took hold in western Europe, 'second sons' of higher nobility became bishops and abbots (often of endowed land). This set in motion significant conflicts over resources (remembering here that these positions were still lordships). With the Gregorian reforms of the 11-12th centuries, the papacy sought to throw off the demands and attributes of secular lordship (private ownership of Church property - the heresy of simony). This was backed by the growing legalistic infrastructure of the medieval Church.
Second and third sons were also becoming lawyers and clerics of the nascent courts (the powerful ecclesiastical courts) of the 12th and 13th centuries (followed weakly by secular courts). By the 13th century, we see a society in western Europe radically transformed into a division between clerics and nobility; often - very, very often - the claims of heresy were used to settle those disputes as the most effective tool for cutting down an enemy. That claim did not happen 300 years before.