Right now, the Quran is organized to be read from the longest chapters (or suras) to the shortest. Is there any reason for why this organization was chosen? Was there perhaps a committee of scholars who debated how the Quran should be written? As I understand, the Quran was passed down orally by those who memorized it (or hafiz) and was not written down until some time after Muhammad's death.
It's worth noting that other religious texts are organized by length as well. The epistles in the bible are arranged by length in the same way.
Nor are the texts strictly arranged by length. From the encyclopedia of Islam:
" Note that Sūra VIII (which is 20th in order of length) and XIII, XIV, and XV (not in this list) are much too short for their positions, while XXXIX, XL, and XLIII are too long. The explanation for these last two groups is clear: XIII, XIV, and XV begin with the “mysterious letters” al(m)r and were kept with the other alr sūras, X-XII, while XL and XLIII begin with ḥm and were kept with the other ḥm sūra s, a group to which XXXIX also belongs (see 4.d below). Other factors that influenced the order of the sūras include their dates, main topics, and introductions. For instance, LVII-LXVI are a group of Medinan sūras kept together in spite of varying lengths (see also their introductory formulas) ; X-XV, besides being alr sūras, all feature prophet stories and are named after prophets, except for XIII, which has almr ; and XXXIV and XXXV begin with the same formula, as do LXV and LXVI, and several groups of sūras with the same mysterious letters (see below); cf. also LXXIII and LXXIV, LXXXV and LXXXVI, and others that begin with oaths."
It's also worth noting that in extremely rough terms, by arranging the Quran from longest to shortest, it is also, generally, arranged from latest revelations to earliest revelations. Muhammad's early revelations tended to be shorter, they have also tended to be more poetical, among other defining features that distinguish earlier suras from later ones.
As for the compilation of the Quran there was a commission appointed by the caliph Uthman. One of the issues, however, is that the process by which this was carried out is extremely unclear. There are modern western scholars who argue strongly that the Suras of the Quran were, in fact, being written down during the lifetime of the prophet. The traditional, religious, account is that, yes, it was passed down completely orally, but in that account it was ultimately written out only twenty years after the death of Muhammad.
Much of the information regarding non-Uthmanic variants is unclear, but yes it does seem that they may have had a slightly different order, and that they may have included additional Suras.
In addition to the Encyclopedia of Islam entry on "al-Ḳurʾān" I would recommend Neal Robinson's "Discovering the Quran" which includes other theories, ideas, and context for why the Quran has the organization and form that it does, discussing various competing ideas and, in my opinion, presenting the most plausible conclusions.
It should be remembered that there were other Qur'an's in former times, according to Muslim tradition, which used a different sequence of surahs (and which excluded some surahs, such as surahs 1, 113, and 114 in today's Qur'an). The codex of Ibn Mas'ud is the best known of these other Qur'an's, and used a surah order different than the Qur'an edition that became dominant.
A physical copy of at least one of these other Qur'an's with different surah orders has recently been discovered (the Sanaa I codex), and has confirmed some of the different surah orders that Muslim tradition had reported for variant Qur'an's (meaning it has some of the special surah ordering transitions that had been reported for Ibn Mas'ud's codex, for example, and which are different from today's Qur'an), although it does not precisely track any of the traditional reports; it has a combination of different surah orders. It appears that Muslim tradition has only reported a fraction of the variation that existed among early Qur'anic manuscripts. Over time, such variant manuscripts were destroyed and suppressed (according to Muslim tradition), and variant readings outlawed, resulting in a much more uniform Qur'anic text, along with the loss of the variant surah orders that had existed in the older manuscripts.
So the order of surahs emerged as sort of a slow evolutionary process rather than as a grand compositional decision. This is why the order of surahs in today's Qur'an appears, to the non-Muslim, as strangely haphazard -- historically the organization of the manuscript was relatively haphazard, with only loose organizing principles at work, and one haphazard version or organizing the surahs ultimately won out over the others.