Is it permissible to go and see a girl for the purpose of marriage in her father's house, before making a decision regarding another previous one, and then to choose between the two?

The basic principle is the prohibition of looking at non-mahrams, except out of necessity or need, such as a suitor looking at his fiancée. The suitor should ensure the woman's suitability for him before seeing her, as his rejection might cause her psychological harm. If a man wishes to marry one of two women and only needs to decide which one he will marry, there is no objection to him looking at both of them in a permissible manner for the purpose of making a definitive decision regarding the proposal.