Praise be to Allah.
We ask Allaah to make it easy for you to find a righteous wife who will be a delight to you. From your question it seems that the family of this girl is a chaste family which protects its daughters, and that is clear from the fact that this girl refused to talk to you and insisted that you should speak to her father, then her father also said that. The father’s attitude is also sound, because he told you that when your father comes and the two families have got to know one another, then it will be possible for you to see her and propose marriage to her if you wish. This is a good attitude because looking at the woman to whom one is proposing, which is permitted in sharee’ah, is only permitted for the one who wants to propose and thinks it most likely that his proposal will be accepted. The great scholar al-‘Izz ibn ‘Abd al-Salaam (may Allaah have mercy on him) said in his book Qawaa’id al-Ahkaam fi Masaalih al-Anaam (2/146), when discussing looking at the woman to whom one wants to propose: That is only permitted for the one who has a strong hope that his proposal will be accepted, not the one who knows or thinks it most likely that his proposal will not be accepted. End quote.
As for getting to know the girl’s family, you can ask about them and ask your father to ask about them. Simply asking about them and consulting others about them before proposing to their daughter is not haraam according to sharee’ah, so it does not matter that this man told you not to ask about them, because in this case speaking and saying something that they dislike is not gheebah (backbiting or gossip) that is forbidden in sharee’ah. Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said in al-Fataawa al-Kubra (4/477), speaking of the kind of gheebah that is permitted with no difference of opinion among the scholars:
The second type is when a man consults others about the person whom he wants to marry or do business with or ask to bear witness, and (the person asked) knows that this person is not fit for that, so he advises him and tells him about that person. End quote.
With regard to how you can find out about her in a manner that is Islamically acceptable: as we have stated above, you can ask about her and it is permissible to look at her if you want to propose to her. If you cannot see her then you should send one of your female mahrams to look at her and describe her to you. It is better if you or the one who is going to describe her to you can see her before you propose, so that you can decide whether to go ahead or not, because looking after proposing may lead to you deciding not to marry her, and that will be upsetting to her and her family. It seems to us that this family will not object to you asking about them and looking at the girl if they see that you are serious about proposing, so you should do what the girl’s father has suggested, then pray istikhaarah and ask Allaah to guide you, and He will decree that which is good for you, in sha Allaah.
As for the qualities that you should look for in the girl whom you choose to be your wife, the Prophet (peace and blessings of Allaah be upon him) has taught us that which the Muslim should seek in the one whom he chooses to be his wife. That may be summed up as follows:
1 – She should be religiously committed, because the Prophet (peace and blessings of Allaah be upon him) said: “Women may be married for four things: their wealth, their lineage, their beauty and their religious commitment. Choose the one who is religiously-committed, may your hands be rubbed with dust (i.e., may you prosper).” Narrated by al-Bukhaari (4802) and Muslim (1466). i.e., that which encourages a man to marry a woman may be one of these four things, but the Prophet (peace and blessings of Allaah be upon him) enjoined us not to choose anyone else over the one who is religiously committed.
2 – She should be fertile, because of the hadeeth: “Marry women who are loving and fertile, for I will be proud of your great number before the other nations on the Day of Resurrection.” Narrated by Abu Dawood (2050); classed as saheeh by al-Albaani in Saheeh Abi Dawood. It may be known whether a virgin will be fertile if she is from a family whose women are known for bearing many children.
3 – She should be a virgin, because of the report: “Why not a virgin, so you could play with her and she could play with you?” Narrated by al-Bukhaari (5052).
4 – She should have a good lineage i.e., be from a good family.
5 – She should be beautiful because that will bring tranquillity to him and be more helpful in lowering the gaze and more likely to bring about love. Hence it is prescribed to look at the woman before doing the marriage contract.
6 – She should be mature and he should avoid foolish women, because marriage is intended to be a permanent relationship and one cannot live with fools, and a foolish attitude may be picked up by the woman’s children.
Finally, we should not omit to point out to you the seriousness of speaking to non mahram women over the internet or via other means of communication, because it is a step that may lead to negative consequences, so beware of the traps of the shaytaan. May Allaah help us and you to do all that He loves and which pleases Him.
And Allaah knows best.