If you se the blockchain.info wallet and set up two factor authentication on your mobile and set up a second password, you'll be safe. Even if you had a keylogger it wouldn't matter with a second password.
Yes I'd recommend the blockchain.info wallet for you for now.
I think however, you are wiser than most newcomers, and have seen it is sensible not to put too much trust in one place.
To "do something" with your CPU, sign up at ypool.net and mine primecoin, (Instruction on site) you can then trade them on BTC-e.com to get a little bitcoin to play with and find out how it all works without exposing your financial info.
Reputable places to buy would be coinbase.com in the US and cavirtex.com in Canada.