An online wallet would work well. I know this question is old but I thought I'd try for a more current answer.
The reason I suggest online wallet, is because you can access it from any computer, browser, smart device, etc.
CoinBase is a great option because you can buy and sell Bitcoin, Ethereum, and Litecoin... so if you mine it and want it in USD ASAP set your miner up with a CoinBase wallet.
Another online wallet is the Blockchain.info's wallet.
These both are great wallets I use and trust, and they also have great mobile applications.
If you'd like to trade your bitcoin on an exchange, I'd recommend either opening a CoinBase/GDAX account (they are linked so if you have money in your CoinBase wallet you can transfer with no fees to the GDAX exchange)
or Bitfinex, which currently is the largest volume Bitcoin exchange out there.
Be warned though, I suggest you use exchange wallets for short term, many large exchanges have been hacked in the past, the best example would be MT. Gox
If you want to play it safe and have the actual wallet on your computer, just download BitcoinCore on to your favorite/most accessible/secure computer. However, you have to download the Blockchain, which takes a bit, but is worth the time and storage for some.