Oi, this is a huge topic (and I can't believe I didn't see the original posting)
First of all, there are several different "theories" associated with reincarnation out there; most Buddhist have the idea that you can come back as an earth worm or rock, etc. depending on you Karma. Too, there is a belief in moving onto higher levels of wisdom and form; look at Buddhist art where you see the bigger and bigger forms of Buddha surrounding the neophyte -- this is an expression of the "Higher-Self vs. the idea of "God".
Most Western European sects believe that we move up the food chain from mineral to plant, to animal and then into human form with even higher forms (forms of greater intellect/wisdom and thus, higher-vibration). They likewise encourage the idea of existing on multiple planes or even places (Yes, like other planets) other than and within our terrestrial state. The tradition stating that we begin as a monad and move forward over tens of thousands of lifetimes.
One thing these two schools tend to share is a "Spirit World School" in which the soul/consciousness goes after physical death so as to learn about the positive and negative aspects of Karma you created in the most recent life. With your Master Teachers & Guides you begin planning out your next life, taking into consideration the many forms of karmic obligation you have in order to bring your personal account into balance -- balance is the key, not the extreme "Light" B.S. we hear everyone in the New Age screaming about. It is during this planning process that you actually do sit down with those entities that a karmic bond exists with; this is where we get tales of a child returning that was once the grandmother or a sibling of an adult. It is also why you will find in various studies, reincarnation tends to connect with specific families and in some cases, the same geographic regions.
I can't find my copy of the article but some years ago Psychology Today ran a wonderful article on this topic that's worth review.
As I've posted elsewhere on this forum, I have some very personal reasons as to why I believe in this particular concept and the rule of Karma, not the least of which centering on the logic that esoterically speaking, it makes far more sense than some old dude with a book and arrogant idea that people need to kiss his glowing tukkis makes all the decisions about who survives eternity and who gets burnt.