nixgeek, that story is a lie, if only for the fact that the Apple logo wasn't an apple with a bite out of it until the Apple II was released.
Before that it was a picture of Newton under a tree. A big, illustrative logo, drawn by Apple co-founder Ron Wayne:
http://img92.echo.cx/img92/9731/ronwayne8rx.jpg
Sites often claim that the Apple name was chosen because:
1. Starts with an 'A' - top of alphabetical lists
2. Apple is an organic, non-computational term, so has a high recall rate when used amongst acronyms and techno-words.
3. Apple has good health connotations (an Apple a day keeps the doctor away)
The current logo, designed by Rob Janoff, has varying explanations. Some say the bite is a subtle link to a "Byte", others say it's supposed to be the dent left in the apple by Newton's head (I find this very hard to believe).
The rainbow is accused of being a relationship with the gay/lesbian pride movement, however the colours are out of rainbow order (often said to mean anarchy, naughtiness). My feelings are that a rainbow was just something else that stood out in corporate identities.
According to popular rumour, the Apple logo was initially plain red (as Apples often are), but was changed to differentiate itself from a tomato. Apparently this was officially corroborated.