transactions – Should a New Address Be Created for Each Transaction?

Yes, the answer is quite logic. Every node has to verify the results of a transaction which invokes a smart contract. The result is that at least every full node will execute the code.

The hash of the transaction isn't relevant until it is being stuffed into a merkle tree. When running the execution, all we care about is the amount of gas, the data being passed in, and the code of the contract that's being called. When the execution completes, the storage tree of the contract may be updated, so we recompute the merkle root hash of that tree (and any other contract which may have been called by that one!)

Source.

MetaMask was recently announced and will be faster than Mist (mentioned in other answer) since MetaMask is a Chrome extension and does not use a local copy of the blockchain.

This video is 3 minutes long, but you have all that you need to get an Ethereum address in the first minute:

https://www.youtube.com/watch?v=6Gf_kRE4MJU

Make sure to keep the 12 words secure and have backups of it. (Also switch to the "main network" if you want to send and receive real Ether.)

Finally, it would still be a good idea to read and familiarize yourself with the "Account Management" and other sections http://ethdocs.org.