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From time to time I find myself listening to someone making a siyum, I am thinking of structuring my learning to pursue finishing enough to make a siyum. But before I commit myself I want to know if that is a noble goal.
So...
Why do we say the "hadran" and other things after completing a sizeable amount of learning (what are the traditional sizes and of what?) Is there a source for this custom? On a deeper, philosophical level what purpose does the siyum have in Jewish life?
Philosophically, the siyyum is a way to celebrate your accomplishment with your community. Especially since the siyyum requires (1) a minyan, so you can say the kaddish derabbanan, and (2) a celebratory meal, it's a way of sharing your personal study accomplishment.
The hadran is one's declaration of intent to return to this subject matter again someday. Just as when we finish reading the book of Devarim on Simchat Torah, we immediately begin again with Bereshit, the idea is that we are completing a phase of study but not, God forbid, completing our study of Talmud without the intent to return.
When I celebrated my fortieth birthday, I timed my completion of learning a masechet of Talmud to make my birthday party be more than a secular-style party; it was a religious celebration as well.
As others have said, the minimum amount of text that justifies a siyyum is dependent on the person's abilities and experience. In my community, the general standard is a masechet (tractate) of Gemara or an entire seder (order) of Mishna; but for those who are first coming to the study of these texts, learning in depth one's first masechet of Mishna is worthy of a siyyum.
This doesn't answer the questions you posted, like "what purpose does the siyum have in Jewish life", but I'll address your first point, whether "structuring my learning to pursue finishing enough to make a siyum" "is a noble goal". Yes, it is. I speak from experience (and relate advice I've heard, too) in saying that having a goal like that in mind will encourage, and thereby help, you to complete the set amount (as long as the goal is realistic). Then, after the siyum, you can set a new goal.
This webpage has a good list of the sources for making a siyum, starting with Abaya in the Gemara (Shabbos 118b):
Abaye said: If I saw a scholar who completed a tractate, then I would make a holiday for the Rabbis.
This document from the Kof-K website (I'm pretty sure it's one of the earlier editions of Halachically Speaking), breaks down the why, when and how we make siyumim.
I heard from my Rebbe R' Yaacov Haber that a siyum is held in honor of a significant achievement in learning - which is measured in terms of the level of the mesayem. For some people, reading through a masechta is an exercise like reading through a newspaper and doesn't merit any special celebration; for others, completing one blatt of gemara is enough of an accomplishment to justify a siyum.
As @msh210 said, the main purpose is probably for goal-setting, to encourage you to make measurable and substantial progress in your learning.
Siyum is traditionally being said after you finish one "masechet" of the talmud or one "seder" of Mishnayot.
More details here: Siyum (Wikipedia).
In the Hebrew version it's much more detailed: סיום מסכת
