Both of these verbs are used for asking about something or looking for information. The nouns for the request / investigation are enquiry and inquiry.
Technically, enquire is used for "ask" in general ("He enquired about prices for the products"), and inquire for a more formal investigation ("The police will make an inquiry into the alleged corruption.")
However, in American English it is now very common to use inquire for everything: "He inquired about prices for the products."
Take a look at your list and see if your desired qualities revolve around the same topic. If you want a man who is creative, passionate, and musically talented, go to local concerts. If you want someone who is athletic, muscular, and energetic, make a stop at the gym. Youll meet plenty of people with the traits that youre looking for. All you have to do is go to the places where your dream man would go. Its that simple.