All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is lawful for a man who is determined to marry a given woman and he is almost certain that she would accept his offer, to look at her, and at some parts of her body to see what will encourage him to marry her. The majority of the jurists are agreed that he is allowed to look at her face and palms several times if he wishes to do so and admire her other attractive features even without permission if he is sure to avoid any sexual desire and without being in seclusion with her. Jaabir narrated that the Prophet said: “If one of you proposes to a woman and he can look at some parts of her body, to see what will encourage him to marry her, then he may do so.” [Ahmad and Abu Daawood]
Jaabir also said: “… I made a proposal to a girl from Beni Salamah and I used to hide (in a place from where I could see her) until I saw from her what encouraged me to get married to her.”
Therefore, it is permissible to look at her in a videotape but under the conditions mentioned above. You stated that in your country there is an engagement period before the marriage contract itself; there is no harm in that. It could even be necessary under some circumstances such as to allow the completion of studies, etc.
However, you should know that the man who proposes to marry a woman remains a non-Mahram to her until the marriage contract is concluded with her. So, he should not stay alone with her or look at her attractive features. All this is forbidden; however, many people have neglected this prohibition.
If there is a necessity to talk to her directly or over the phone, then this is allowed but in the presence of one of her Mahaarim (unmarriageable men). Such talks should be far from anything that could lead to temptations and their causes.
We ask Allah to grant you success in finding a pious wife who will be a comport to your eyes.
Allah knows best.