Babies learn by play and imitation. Children learn by play and imitation. There is no reason this isn’t the easiest way for adults to learn, as well (and I speak as someone who has made a successful career of using board games to teach business finance rapidly and enjoyably).
The imitation of language, with a baby learning to speak, is enhanced by repetition–not just simple sentences and phrases used again and again, but also lullabyes and nursery rhymes. The advantages to songs and poems are that they are engaging to the ear (even if the words are not understood); that they are repeated virtually identically each time the same person sings or recites them; that the repetition and music, the rhythm and rhyme, make it easy to learn; learning then moves from passive (understanding) vocabulary to active (speaking) vocabulary; and the word-for-word learning teaches the structure of the language, the syntax, the grammar, as well as basic vocabulary and playful other words.
The principles are no different for someone learning a second language, whether as a child or an adult. To make the process engaging, to develop active use of the language with a confident vocabulary and grammar, there is nothing better for the beginner than songs and poems. Recorded music is fine–then the repetition will always be exact, and learning to sing simple songs (The Beatles’ ‘Hello Goodbye’ comes to mind) will contribute to developing a native speaker’s accent. With ESL–English as a Second Language–you may need to decide if you want the Queen’s English, or Liverpool, or Nashville, or what.
But singing isn’t always a practical solution. In that case, look at the resources developed for ESL teachers. Here is a webpage developed by the British Council and the BBC. And here for teens and adults is an excellent website with ‘Popular Poems to Teach‘. Note that most of the poems (though not all) whether British or American are using rhyme and metre. And this, again, is because those factors make it easier to learn things by heart–and that is what songs and poems will achieve: learning not just words and rules, but rather entire sentences with their grammar and vocabulary, learnt by singing or reciting, far more enjoyably than by studying lists and charts.
And the advantage is universal. Songs and poetry are part of the human experience, whether you come from China, India, Saudi Arabia, Nigeria or Brazil. Learning to sing or recite in English is not to start again from scratch, but to enjoyably refresh a childhood experience, a skill that has already been mastered.