"I like this song."
Translation:मुझे यह गाना पसंद है।
Both sound valid for a native speaker. I might use your sentence if i want to emphasize on "यह गाना" rather than "मुझे". There's a lot of ways to flip around the words in Hindi sentences and still have it make sense. E.g. "पसंद है मुझे यह गाना" is valid too, if I want to stress on the verb "पसंद" more than the other parts of the sentence.
गीत and गाना are synonyms, but since गीत is part of Sanskritized Hindi, it has a more literary feel and isn't as common in daily conversation. Noun usage often varies by region and the Hindustani family of languages, even though mutually intelligible, sometimes have different words for the same thing e.g. from other local languages / Arabic / Sanskrit / European languages. That's why synonyms are extremely common in Hindi.
a valid sentence might be "maine yah gaana pasand kiya", but that changes the meaning a bit. maine and mujhe are not interchangeable. "maine" is used for past or past perfect verb tenses. maybe another valid sentence for the present tense is "maine yah gaana pasand kiya hai", which emphasizes the self-pronoun over the verb, and changes the connotation of "pasand" from "to like", to "to choose/select".