There are many places to get Bitcoins, but we recommend BitPanda.com, especially if you live in EU. Besides credit cards BitPanda also supports SEPA, SOFORT payments, through which Bitcoins can be purchased via regular online banking.
You will also need a wallet to store your Bitcoins. If you prefer your wallet to live in your computer we recommend MultiBit. If you would like a cloud based wallet we heard good things about BlockChain.