Moshav Zekenim #1: Amalek is called "Reishis Goyim" and in the end, he will be destroyed - as implied in Balak Bamidbar, 24:20. We are commanded to bring Reishis Bikurim and to destroy Reishis Amalek.

Moshav Zekenim #2: Amalek cut off Yisrael's Milos and threw them into the air (Rashi in Devarim 25:18) - to prevent them from creating Peiros (having children), so we bring the first-fruit from our land to Hashem. ¹

Ba'al ha'Turim: a. Because the juxtaposition of "Vehayah ki Savo el ha'Aretz" to the Parshah of Amalek hints that the Mitzvah of wiping out Amalek applies from the moment ² Yisrael enter Eretz Yisrael; ³ b. Because Parshas Bikurim contains "Arami Oveid Avi" - with reference to Lavan, and Amalek was the one who informed Lavan that Ya'akov had fled.

Oznayim la'Torah: Since the prime function of Amalek is to create Bitul Torah - to stop Yisrael from learning Torah - Indeed, he attacked them when they left Egypt because they were lax in Torah-study. ⁴ Therefore we counter that by bringing Bikurim (and Terumos and Ma'asros) to the Kohanim and the Levi'im, who are the teachers of Torah ⁵ - to enable them to teach Torah to Yisrael. ⁶

Sifri: To teach us that one should be careful to perform the Mitzvah of Bikurim, since it is on the merit of Bikurim that they will enter Eretz Yisrael. ¹

Rashi: It implies that the Mitzvah of Bikurim will only come into effect ¹ after they have conquered the land and distributed it. ²