All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
As a man is required to choose the righteous and well-mannered woman to be his wife, a woman should also look for the same qualities. If Sharee‘ah criteria are met in terms of choosing one’s spouse, the marital life will be full of goodness and this will be reflected on the offspring.
Hence, if you can convince this suitor to adhere more to religion by offering congregational prayers at the mosque and stop listening to music, then it is permissible for you to marry him. Otherwise, it is better not to marry him if you are likely to be proposed to by another person.
You will not be sinning if you turn him down because he does not offer prayer in congregation without a valid excuse and because he listens to music.
Allaah Knows best.