Common (and good) ways to ask for hand in marriage
I can't find a Chinese song named '今天你要嫁给我好吗'.

Is it "今天你要嫁給我" by 陶喆 ?

Considered about the sentence "今天你要嫁给我好吗", I think  "今天你要嫁给我吗" or "今天嫁给我好吗" are better. "你願意嫁給我嗎?"is smooth and clear too. However, adding "今天" is more pressing.

In fact, in the song '今天你要嫁給我', it used '今天嫁給我好嗎' as a question.