What are the legitimate means for a young man to search for a righteous wife, and is it permissible for him to ask for a picture of a girl with the aim of getting to know her for an honorable purpose?

The legitimate method of marriage is what the Prophet's Sunnah has clarified: looking at the fiancée and proposing to her through her guardian. Al-Tirmidhi narrated from Al-Mughirah ibn Shu'bah that the Prophet, peace and blessings be upon him, said to him when he proposed to a woman: "Look at her, for it is more likely to engender affection between you."