Don't listen to JayChou, even a native Chinese can not understand it.

May-Day(the do pop and some country rock but do tend to be slightly unclear in pronounciation at times, much better than jay chou though)

FIR飛兒樂團

SHE

following are famous song singers that I liked, might be better since they do have good pronounciation(yes I'm too old to be listening to pop music...)

a-lin
Eason Chan

江蕙

蔡琴

齊豫

rock：摇滚乐

崔健：一无所有、花房姑娘、新长征路上的摇滚

黑豹乐队：无地自容

郑钧：回到拉萨、赤裸裸

零点乐队：粉墨人生、玩儿够了没有、相信自己

唐朝乐队：回到唐朝、国际歌

张楚：孤独的人是可耻的、姐姐

何勇：姑娘漂亮

汪峰：北京，北京

张岭：北方过客

new ones:

许巍：蓝莲花

gala：追梦赤子心

逃跑计划：夜空中最闪亮的星

李荣浩： 模特                   very popular now（not rock）

陈奕迅：十年、k歌之王（Eason     not rock）

周杰伦：双截棍（difficult but fantastic）、听妈妈的话、黑色毛衣、简单爱（Jay chou）（not rock）

old ones（not rock）：

邓丽君：恰似你的温柔

张学友：祝福、情书、情网

刘德华：冰雨、忘情水

姜育恒：再回首

郑智化：水手、星星点灯

罗大佑：童年、你的样子、亚细亚的孤儿、弹唱词

李宗盛：领悟、山丘

走在乡间的小路上

王菲：相约九八、给自己的情书

动力火车：当、第一滴泪

屠洪刚：霸王别姬、精忠报国

那英：征服、一笑而过

刘欢：好汉歌、千万次地问

BEYOND was popular in china，but their language is cantonese.

don't care about listening,just enjoy it.

no one could say no to my recommendation，I think.

Jay Zhou's song is difficult for Chinese,Not to mention foreigners

I recommend Taiwan's famous rock band- MAYDAY

(wu yue tian). It's easy to find them out on youtube. I think their songs are catchy and have wide range of styles. 

Hope you enjoy it!