I'm using a greenaddress.it wallet, but assume this will be the same for all deterministic wallets. (If not, please correct me!)
Since the first and all further bitcoin addresses my wallet will ever use can be determined by the "mnemonic passphrase", is there anything else I need to backup / store securely?
For all wallets, which support BIP-0039 (still draft status), the mnemonic passphrase is enough to completely backup your wallet. As I can read from the greenaddress.it website they support BIP-0039 (not tried), so all you need is the passphrase (seed).
Theoretically, you can import the seed into any other wallet implementation and manage your bitcoins from there. However e.g. the popular Electrum wallet doesn't comply with BIP-0039. So you have to take care if you want to switch wallets.
For a detailed understanding of deterministic wallets, I can only recommend you reading the section on wallets in the book "Mastering Bitcoin".
