What is the ruling on the wording of the supplication: "O Allah, You are my Guardian and my Disposer of affairs. I have entrusted my matter to You, so choose for me, then make me content with what pleases You," and is it permissible to supplicate for marriage to a specific person?

There is no harm in supplicating and asking Allah to choose for you. There is also no harm in asking Him to marry you to a man of good religion and character, and to answer your prayer. It is also permissible for you to offer yourself to him through one of your mahrams (unmarriageable kin) or one of his mahrams. It is advised to be diligent in reciting the prescribed supplications.