Jonathan Edwards’s thought on the relationship of self-love and the believer’s love for God can be best summarized, I think, in this paragraph from Religious Affections*:
…the exercises of true and holy love in the saints arise in another way. They don’t first see that God loves them, and then see that he is lovely; but they first see that God is lovely, and that Christ is excellent and glorious, and their hearts are first captivated with this view, and the exercises of their love are wont from time to begin here, and to arise primarily from these views; and then, consequentially, they see God’s love; and great favor to them. The saint’s affections begin with God; and self-love has a hand in these affections consequentially, and secondarily only. On the contrary, those false affections begin with self, and an acknowledgement of an excellency in God, and an affectedness with it, is only consequential and dependent. In the love of the true saint God is the lowest foundation; the love of the excellency of his nature is the foundation of all affections which come afterwards, wherein self-love is concerned as an handmaid: on the contrary, the hypocrite lays himself at the bottom of all, as the first foundation, and lays on God as the superstructure; and even his acknowledgement of God’s glory itself, depends on his regard to his private interest (in Yale-Works 2:246).
For more on this topic, you could also read this post over at the Luther’s Stein blog.
*Admittedly, for this paragraph to be the best summation it should have included a word about the work of the Spirit in generating man’s love for God.