Don't use bitcoin qt then. I agree it is a bit of a ballache for new users but I don't really think there's any need to use it with all the lite clients we have nowadays. Get one of them or a blockchain.info wallet and you're good to go immediately.
No, I will never leave my coins and private keys on a website I don't control. Maybe that's fine for people who use small amounts of Bitcoin, I use hundreds of thousands of dollars worth of Bitcoin so it simply isn't an option.
I'm going to have to go ahead and advise against storing hundreds of thousands of dollars worth of