"My Wallet" at
https://blockchain.info/wallet/ has already been suggested and is good for beginners. Enabling the two-factor authentication option is recommended for security.
If you have a little patience and are really keen on Bitcoin and thus eager to assist the Bitcoin network,
and assuming you have reasonable computing resources to hand, i.e. no ten-year-old laptop running XP like molasses in the Yukon (in January during a cold snap!), then download Bitcoin-Qt from
http://bitcoin.org/ (follow the links), install it, wait for the blockchain to sync up
et voilà! The more you have this program running, the more you are assisting the network as a
full node.For storing more than pocket change worth of bitcoin,
an offline wallet is the best and safest option. "Hot" wallets running live on your internet-connected computer are as secure as your computer itself. Beware viruses/malware!