I think if you want to learning Chinese by singing songs, you should choose some simple but nice songs. here’s my list:
情人的眼泪 by 蔡琴
月亮代表我的心 by 邓丽君
我只在乎你 by 林宥嘉 （originally by 邓丽君）
夜来香 by 李香兰
标准情人 by 金城武
朋友 by 周华健
一个人 by 任贤齐
心太软 by 任贤齐
还有我 by 任贤齐
练习 by 刘德华
简单爱 by 周杰伦
相思河畔 by 陈百强
all those songs are old stuffs. and as said above, KTV is a nice place for you. 😀