1) The Beis Ya’akov of Ishbitz points out that the idea of bikurim is reflected in the root of the word: b-k-r. The letter beis is the second letter of the first unit of 10 in the aleph-beis; the letter kaf is the second letter in the unit of the next 10; the letter reish is the second letter in the last group. B-k-r is all about coming in second. The farmer says, “Hinei heiveisi es reishis pri ha’adamah,” these are my first fruits, but the truth is that before he even planted the seed from which those fruits grew there was an earlier reishis, the reishis of Hashem’s plan for these seeds to grow for this farmer and be used for this purpose. When the farmer brings those first fruits to the Beis haMikdash, he reminds himself of the real reishis.
2) Rashi comments on the word “reishis” in the pasuk, “V’lakachta mei’reishis kol pri ha’adamah”:
לא כל ראשית, שאין כל הפירות חייבין בבכורים אלא שבעת המינין בלבד
The Mizrachi makes one little change in the girsa -- he takes out the letter “shin” before the word “she’ain...” – but boy, does changing that one letter make a difference. According to Mizrachi, Rashi is making two separate unrelated statements: 1) you can’t designate an entire field as bikkurim, i.e. there has to be something leftover after you take off the reishis; 2) only the seven minim are obligated in bikurim.
What’s motivating Mizrachi here is the parallel between this Rashi and another Rashi. In the parsha of hafrashas challah Rashi comments on the words “mei’reishis arisoseichem” (Bamidbar 15:21) that challah must be “miktzasa v’lo kulah,” i.e. it is a piece that is taken off from the batch of dough, but it cannot be the entire batch. Here too, according to Mizrachi, bikurim must be “mei’reishis,” part of the crop, but one cannot designate the entire crop or field to be bikurim.
Maharal in Gur Aryeh disagrees and says a lomdish chiluk. There is an issur of tevel that prohibits eating the food before challah and terumah are taken. The hafrasha of terumah and challah is a matir - it comes to remove that issur; therefore, there has to be something leftover upon which the matir is chal. Not so bikurim. There is no issur of eating the crop before bikurim have been taken off – it’s a mitzvah to tak bikurim, but it’s not a matir of anything. Tosfos (Bava Basra 81) writes that bikurim are a chiyuv on the person, not on the fruit.
The MG”A (O.C. 8 - posted on this in 2006 in piece that needs rewriting ) asks how it is that woman sit when they recite the bracha on hafrashas challah when birchos hamitzvah are supposed to be recited while standing. He answers that there is a difference between mitzvos like challah and shechitah and other mitzvos. The MG”A might be alluding to this sevara of the Gur Aryeh: hafrashas challah is a matir, not a mitzvah in its own right. (See this post as well.)
3) The halacha is that a person cannot appoint a shliach to bring his bikurim to the Beis haMikdash – he has to deliver them himself. A shliach cannot give thanks for “ha’adamah asher nasatah li,” as is the nusach recited when bringing bikurim, if the bikurim are in fact not the fruits of his land but of someone else’s. I would suggest that this is not just a technical issue with the nusach, but says something fundamental about the nature of the mitzvah. If I remember correctly (sorry, I didn't double-check), the Avudraham writes that the reason we say modim derabbanan alongside the chazzan’s recitation of modim during chazaras hashatz is because the theme of modim is giving thanks. Saying thank you is something that must be done personally, not via a shliach. Here too, the purpose of bringing bikurim is to give thanks to Hashem for giving us Eretz Yisrael and its crops. It has to be done in person by coming to the Beis haMikdash, not assigned to a shliach.
4) Since we (Ashkenazim) will IY”H start saying slichos this motzei Shabbos I wanted to highlight the Meshech Chochma’s observation that there are exactly 13 mentions of the shem Hashem in the parsha of bikurim which he says correspond to the 13 midos ha’rachamim. Interestingly, if you look at Shmos 34 where the 13 midos appear, theataliya ends with the mitzvah of bikurim. What are we supposed to make of this observation I don’t know, but it’s something to think about over Shabbos.