So many songs here, could anybody give me some advices which songs should I start with for self-learning these Chinese characters?

Hi Wendy, you may start to learn with the following songs.

Olive tree	     橄榄树          Gǎn lǎn shù	

Health song         健康歌          Jiàn kāng gē

Small town girl    小镇姑娘      Xiǎo zhèn gū niang	

Please ignore how fast the songs are, just focus on studying these Chinese characters of lyrics with the online flash cards and the typing game, which are very very common Mandarin. e.g. 爷爷(yé ye, grandpa)，左(zuǒ,left)，右(yòu,right).