Phoebe is definitely meant to be more New Age-y, which is how the character originally started out, until they made her into the archetypical dumb blonde. Rachel and Ross were Jewish (her name is of Biblical origin) and I'm sure the relationship was already decided on when the pilot was made and the characters were being named, so the alliteration was probably intended to evoke the feeling that they belonged together.
Monica is Ross's sister but they are children of a mixed marriage so she ended up being the more Christian of the two (you see her with a tree, and making nonkosher food, plus she ends up marrying a gentile, whereas Ross, while he does date and marry gentiles, is the only consistent intellectual in the group, and also a bit of a shlub -- look the word up). Joey, the stupidest of the group (if Joey were a real person, he'd be too dumb to survive on his own, and Phoebe is not much better), is also meant to be straightforward Italian. He's getting by with acting because he has looks, because if he didn't, he'd be mixing concrete. He's the male version of the dumb blonde.
Chandler is meant to be tightly wound so he has a very formal name. Plus he also comes from some money and he's not supposed to be ethnic in any way, so that all works together.
The backstories (probably except for the eventual Chandler-Monica romance) were, I'm sure, mainly written by the end of the first season or even earlier. I'm not saying that all of the plotting was done by then, but writers for sitcoms, because they have to pump out a lot of product, need a detailed framework. The characters have to be well-known to the writers, even if the details are not known to the audience (yet) as that makes the writing easier and helps to keep it more consistent.