Is it recommended to have an agent for marriage, or should a Muslim undertake it himself? And what are the examples of the righteous predecessors in this regard?

A person's direct handling of contracts is better than appointing an agent, if they are capable, so they may know what is incumbent upon them, what is theirs, and what is due from them. This is what the Prophet, peace and blessings be upon him, and his Companions did. Nevertheless, there is no harm in appointing an agent, for the principle "the action of another by his command is like his own action" permits it.