A man can't discard his young children, or starve them:
כתובות סה ב
דרש רבי עולא רבה ... אע"פ שאמרו אין אדם זן את בניו
ובנותיו כשהן קטנים אבל זן קטני קטנים עד כמה עד בן שש
Rabbi Ula Raba said... although they said the a man is not obligated to feed his young sons and daughters, he must feed his very young sons and daughters. How young? Until the age of six.
The condition of daughters from marriage is slightly better:
משנה כתובות ד יא
בנן נוקבן דיהוין ליכי מנאי, יהויין יתבן בביתי ומתזנן מנכסי עד דיתנסבן
Mishna ktuvot p4 11
[One of the marriage conditions written in the Ktuva is:]
Daughters that you will have from me, will sit at my home, and will fed from my property until they we be married.
That's only until their puberty.
Also, a man must teach his son a profession:
קידושין כט א
ת"ר והאב חייב בבנו ...וללמדו אומנות
Our Rabbies said: Father obligation to his son... and teach him a profession.
About "transferring rights for gain" part:
A man can marry his young daughter to other, but I believe that the premise is that he is doing it for her own good (he can't support her, etc), doing it for gain is being *&^@%#.
A man can sell her for maid (Which is, again, for marriage. The master or his son must take her, or she is freed) only at the most dire situation:
רמב"ם עבדים 4:2
אין האב רשאי למכור את בתו אלא אם כן העני, ולא נשאר לו כלום--לא קרקע,
ולא מיטלטלין, ואפילו כסות שעליו; ואף על פי כן כופין את האב לפדותה אחר
Rambam Laws of Slaves 4:2
"A father is not allowed to sell his daughter unless he became impoverished and had nothing, not land or chattel or even a shirt on his back, and even after selling her we force him to buy her back if he can."