Why does the Torah add the word "v'Chol Terumah"?
Rashbam: It comes to incorporate the Terumah Gedolah and Terumas Ma'aser that the Levi separates. 1
It is the Kohen who must go to the granary to receive Terumah; so why does the Torah write "v'Chol Terumah asher Yakrivu la'Kohen"?
Ramban: R. Yishmael asks that the Pasuk cannot discuss Terumah, since "Yakrivu" is used exclusively for something that is brought on the Mizbe'ach (See Ramban, DH 'v'Od Shanu', who elaborates).
What does this Pasuk teach us?
Ramban #1: It teaches us that, once one gives the Kohen Terumah Gedolah, it belongs to him, and whoever steals it from him must bring an Asham Gezeilos. 3
Ramban #3, Moshav Zekeinim (citing the Sifri): The Torah does not give a Shi'ur for Terumah. Our verse teaches that whatever one designates as Terumah takes effect and he must give it to the Kohen - the Kohen may not take forcibly - and he must leave some over. He cannot designate the entire granary to be Terumah.
Seforno: One brings the first-fruits to the Owner of the land - Hashem, who hands them to the Kohanim of that Mishmar, just as He does with Gezel ha'Ger (Refer to 5:8:2:1).
Ramban: Which explains why the Torah inserts it here.
In Pasuk 10, and the law of Ma'aser Sheini and Ma'aser Beheimah it taught in Vayikra 27:30 (Ramban).
QUESTIONS ON RASHI
Rashi writes that the verse teaches that one gives Bikurim to a Kohen. We learn from this "Bikurei Kol Asher b'Artzam...Lecha Yihyeh" (18:13)!
Moshav Zekeinim: Our verse uses an expression of Hakravah to teach that one must give to the Kohen from hand to hand, and he is credited as if he offered them on the Mizbe'ach. One who gives a gift to a Chacham is like one who offered Bikurim (Kesuvos 105b).
Moshav Zekeinim #2: The verse below (18:13) teaches that Bikurim apply attached to the land, unlike Terumah. "B'Artzam" implies attached.
Moshav Zekeinim, citing his uncle: The verse below (18:9) teaches that Bikurim is the Kohen's money; he may be Mekadesh a woman with it. 1
Moshav Zekeinim #3: Our verse teaches primarily about Terumah. Refer to 5:9:3:1,2,4.
Moshav Zekeinim: I disagree. We know this already, for it is called Terumah (Yevamos 73a)!