There are any number of sources of Chinese pop music to integrate into your studies (for example, see the post on Chinese radio iOS apps), but unless you are quite advanced, it will probably be difficult to make out most of the lyrics 歌词. Here are some sites with a selection of lyrics in pinyin and hanzi. Each takes a different approach to the display of the lyrics and how English is incorporated, if at all.
The website chinese-tools.com has a selection of songs with lyrics displayed in simplified characters with interlinear pinyin. This arrangement is like ruby annotation and let’s you easily follow both hanzi and pinyin while listening. It utilizes tool-tip type pop-ups to let you see English translations of individual words (although some words seem not to be linked). Audio files (mp3 and/or wav) are available for download (legally, I hope); YouTube videos are embedded at the bottom of the page (not visible in the image).
The website singklyrics.com has videos captioned for karaoke 卡拉OK. The changing color makes it easy to follow the hanzi captions while listening to the song. Below the video are lyrics in pinyin, but unfortunately without tone marks. It seems that most of the videos are captioned in traditional characters; simplified characters can be swapped for the pinyin by clicking the tab labeled “Chinese”.
Finally we have chinese-mp3.com. This site shows hanzi and pinyin in parallel columns. Clicking a “translate” link will add a column with English, but it seems to be a machine-translation and hence of variable quality.
Find Chinese pop on iTunes.