Did He promise to take them out on the first day?
Radak: Yes - "Lachen Emor li'Vnei Yisrael Ani Hashem v'Hotzeisi Eschem" (Shemos 6:6).
Malbim: From that day He distinguished them to be under His Hashgachah, and to take them out with signs and wonders.
Why does it say "Asher Tarti Lahem"?
Malbim: This is like one who has a lovely plant - he seeks for it Keren Ben Shamen, a place where it will succeed to be a choice vine (based on Yeshayah 5:1-2). Hashem chose Eretz Yisrael, which is "Zavas Chalav u'Devash" (Shemos 3:8) - they will find their physical needs there, and be free for Torah and Avodah..
What is the meaning of "Tzvi Hi l'Chol ha'Aratzos"?
Radak: It is glory and treasure to all lands. It is the middle land, better than other places. Its air is blended and better than that of all lands - "Yefe Nof Mesos Kol ha'Aretz" (Tehilim 48:3).
Radak citing Targum Yonasan: It is praise to all lands.
Malbim: It is the most desired land for matters of the Nefesh, spirituality, Shechinah, Hashgachah and Nevu'ah.
