Clerics, Page 31, PHB,
"Some deities have favored weapons (see Deities, page 90), and
clerics consider it a point of pride to wield them. A cleric whose deity’s favored weapon is a martial weapon and who chooses War as one of his domains receives the Martial Weapon Proficiency feat related to that weapon for free, as well as the Weapon Focus feat related to that weapon."
Spiritual Weapon, Page 256, PHB,
"The weapon that you get is often a force replica of your deity’s own personal weapon, many of which have individual names. A cleric without a deity gets a weapon based on his alignment. A neutral cleric without a deity can create a spiritual weapon of any alignment provided he is acting at least generally in accord with that alignment at the time."
Combining the two seems to indicate the cleric would get whatever weapon is closest on the chart from page 256. That's my interpretation.