https://www.coinbase.com/ works fine, but I wouldn't suggest it due to past issues with coinbase.
I would use https://blockchain.info/wallet
You should be fine with coinbase for the most part, but if you deal with any fishy people I would use blockchain.
Regardless; you don't need to confirm your identity at all on blockchain but you do have to provide a name on coinbase. Your account won't be limited at all on coinbase without a verified identity. However, you can't buy or sell bitcoins on coinbase without confirming your identity. You can just receive btc and then send btc. Not buy btc from coinbase and then sell btc to coinbase. You'll have to get your own btc elsewhere if you're planning on doing that.
As for the sending and receiving part of btc, basically if you're sending btc you'd go to the send money tab and put their wallet address in
Blockchain:
http://i.imgur.com/oiLV3Qt.png
Coinbase:
http://i.imgur.com/WqD0qN5.png
For receiving btc, you would give them your wallet address which is either a scan code or something like this 18sJkUdhdhE75hdmsaje5FgsjhRTxk.