How would I go about exploring Bitcoin's entire block chain?
The easiest way to look at the transactions in any arbitrary block would be with a block explorer. 

As of the instant I'm answering this question, the newest block is block #456238, so you can peek at any block by creating an address for a web block explorer as follows (Blockchain.info for illustrative purposes):

https://blockchain.info/block-height/0

https://blockchain.info/block-height/456238