The Analects as it currently exists is a hybrid work and not the work of a single hand. In the Han dynasty it seems to have been widely known that there were at least two different versions of the work, associated with the states of Lu and Qi respectively; the Qi version seems to have had a couple more books, but the books of the Lu version seem to have contained material not in the Qi version. These two versions were put together by the scholar Zhang Yu, probably to facilitate his work as tutor to the Imperial family; Zhang Yu used the Lu version as the primary base but added other material from the Qi version. This is the received and preserved text of the Analects that we have today. The Analects are not, however, the only source of old stories about, and sayings attributed to, Confucius, although most scholars seem to agree that the Analects is the most credibly authentic source, with roots going back at least to his student's students.
All of this raises the question of how best to read the work. I think the best way, at least for a crude preliminary reading, is simply to place the emphasis on Master Kong as teacher. It's a teaching book built on a teacher's practice, preserved through the ages by teachers. This is a reason why its apparent disorder does not in any way hamper its qualities; it's a collection of things to make you think, or, perhaps more accurately, to reflect and study. It may well be more; but that seems a good place to start.
The translation I'll be using is Raymond Dawson's. In his introductory notes he points out that, despite the fact that our temptation is to read the whole work with ponderous solemnity, many of the passages seem to be humorous, and were probably preserved in part because of the wit. Catching humor through translations is tricky, but it's worth trying, since humor is part of teaching, and some of Master Kong's comments are quite funny:
Ji Wen Zi thought three times before acting. When the Master heard of this, he said, 'Twice will do.' (5.20)
And that joke seems a good motto for starting out in any enterprise.
Book I begins and ends with a comment about how it is important not to worry about whether others appreciate you; the truly noble are not resentful of the failures of others to recognize their qualities (1.1) and the real worry is not whether your qualities are being recognized but whether you are recognizing the qualities of others (1.16). In 1.1 this is linked to the two important ideas of learning and friendship. Proper learning is in great measure about keeping one's priorities straight. Appearances and mere verbal cleverness distort our growth (1.3). Master You and Master Zeng, two other teachers we meet in Book I (and likely important people in the early schools in which the sayings of Confucius were transmitted), show this as well, with Master You emphasizing that the noble will start with the root (1.2) and Master Zeng giving us his daily examination of character (1.4): Am I loyal in dealing with others? Am I trustworthy in dealing with friends? Do I practice what has been handed down to me?
To learn with the right priorities is to develop ren, humanity towards others. This begins with our duties to our parents and siblings (1.2; 1.6); Master Zeng notes that the ramifications of this putting family first are much wider than ourselves (1.9). If someone builds on this and acts well toward others, Zixia, a student of Confucius, remarks, then that person has some right be called learned even if he is completely uneducated (1.7). Loyalty (zhong) and sincerity (xin) are the matters of fundamental importance (1.8, 1.13). The standards can be quite high (1.11; 1.12), and they require positive and not merely negative action (1.15). All of this is a matter of learning, though, so much so that the noble may be summed up in a single phrase: "fond of learning" (1.14).