BitCoin is entirely placed in the first camp. It was not designed to be backed by anything real. It only claims to be decentralized and have a level of inflation more predictable than anything else.

You can accept payments now. You don't need to wait to generate a coin. You do need to wait to download the entire block chain, which could take a few days. You'll know it's done when the number in the lower right of the BitCoin window has stopped incrementing.

Here are some places where you can spend coins:
http://www.bitcoin.org/smf/index.php?topic=30.0

See:
http://www.bitcoin.org/wiki/doku.php?id=block

You do lots of SHA-256 hashes of a random number until the hash result is less than the network's current target number. This happens at a predictable rate, and when it does, you win a certain number of BitCoins.

Also the technical paper:
http://www.bitcoin.org/sites/default/files/bitcoin.pdf