What is "Reishisam asher Yitnu la'Hashem" coming to include?
Rashi: It comes to include Terumah Gedolah. 1
Ramban (in Devarim 18:3, citing the Sifri): "Reishisam" comes to include Reishis ha'Gez, "asher Yitnu" - Zero'a, L'chayaim ve'Keivah, and "la'Hashem" - Chalah.
Which is called "Reishis", because it precedes Ma'aser Rishon (Rashi Eruvin, 31b). Refer also to Devarim 18:4:1:1*.
Why does the Torah refer to Terumah as "Reishisam"?
Rashi (in Eruvin, 31b): To teach us that Terumah Gedolah precedes Ma'aser - which one separates from what remains after Terumah has been separated. 1
Why does the Pasuk insert the word "Cheilev" (the best) by each of the fruits?
Rashbam: This is based on Pasuk 30, where the Torah writes that one should give "Cheilev" when separating Terumah. 1
B'choros, 53b & 54a: To teach us that one must give Cheilev of each one separately - and not from opne on to the other. And "Reishisam" teaches us that the same applies to wine and corn and to two species (wheat and barley) of corn. 2