Storing an encrypted private key on a server
I am planning on building a small e-wallet website to learn the basics of encryption and handling accounts, transactions, and balances in Bitcoin.


This is really not the place to learn. Even the most hardened Bitcoin services get attacked on a regular basis. 


  Using brainwallet, the process for account creation is this:


"Brain wallets" are an incredibly easy way for users to lose all of their funds. It happens every day. Think your 8 word sentence is strong enough? Chances are that it's not, and there's at least three bots that will empty the wallet in seconds of it receiving funds. 


  Now, whenever a user wishes to spend a transaction on my site I am attempting to use brainwallet to send transactions.


The code you're referencing is just a frontend for blockchain.info and the bitcoinjs library. 


  As a side note: is this a sound process for storing and transmitting data to the server?


Blockchain.info uses this method for it's web wallet, but no, it's very unsafe and offers very little in the way of security. If your server is compromised, the keys still are. If you are malicious, you can just backdoor the client scripting and nobody would ever know. It is not secure, and a service using this type of system shouldn't be advertising itself as such.