For opening an Austrian bank account you need a valid personal ID card, passport or driving licence. It is advisable to open a current account (an account to which your salary is paid; "Gehaltskonto").
Most banks now offer an online banking service, which can be a convenient way of managing your finances. If you do open an online bank account make sure that you have the necessary security measures on your computer, and never disclose your user name or password by email.
More details are available at banks. An overview of bank conditions for current accounts can be found on www.bankenrechner.at/girokonto or www.bankkonditionen.at/produkte/gehaltskonto.cfm (in German only).