Now, i assume (perhaps in error) that the mtgox's and blockchain of the world have better security than i can privide while allowing me to receive/send bitcoins.
I believe this is an erroneous assumption. At this point in the growth of bitcoin, you simply can't trust anyone else to hold your coins for you. IMHO, the main reason that bitcoin businesses can't and that banks can boils down to two simple issues: insurance, and the nature of the money itself.
There are no bitcoin insurance companies yet. So if Mt. Gox gets hacked and loses all of it's bitcoins, everyone--you, Mt. Gox, and all their customers--are just out of luck. And while every hacker on the planet knows about Mt. Gox, and knows they hold millions of dollars worth of bitcoins, very few know about any bitcoins you keep stashed away yourself, so the risks to Mt. Gox's bitcoin stash are far greater than the risks to your own. This will likely change as bitcoin continues to grow, but yes, currently this is an advantage banks have over the bitcoin network.
The second issue, the nature of the money, is something that simply isn't going to change, because of the way it all works. Bitcoin is different from the fiat banking systems, with advantages and disadvantages. The only way bitcoin will have those disadvantages removed is to use an infrastructure built on top of bitcoin that changes it to effectively act like the traditional banking system. It's an either-or thing; you can't have the advantages without the corresponding downsides.
All that said...
If I do not keep them online anywhere, how does that work? Do I send all the accumulated coins to my private wallet every hour, and then make a cd backup of that wallet every hour?
Ideally, you would design (or have designed for you) a system that does exactly what you expect Mt. Gox or blockchain.info to do, but does it more securely, and in secrecy. This isn't a monumental undertaking; Bitcoin-Qt is already designed to process most of what you need, the backups and redundancy is routine, and there are extra tools to help with security (Armory comes to mind.) But of course, it's going to cost some money and involve some effort setting up and handling the hardware, just as if you wanted to custom-design and run your own website rather than letting someone else build and run one for you.
It sounds like that's what it will take to securely do what you want to do with bitcoins.
Regardless of how I use the coins, the question is the same: What is the best way to make an online wallet secure?
Yes, there's a way to make an online wallet (more) secure. You mainly do it by not having your private keys online. You setup a server that checks and processes incoming transactions, dispenses pre-generated payment addresses, and creates unsigned transactions for spending the bitcoins. Then you transfer those unsigned transactions to an offline system that has the private keys, and checks and signs them; you then transfer the transactions back to the online system to be broadcast. There are a number of ways to do the transfer, and ideally it would require physical movement of a file and manual authorization each time, but that's the basic idea.
If that doesn't fit into the time constraints of your system (you HAVE to have automated spending of the bitcoins, you don't want customers to have to wait to pull out funds,) you could keep a "hot wallet," but keep the bulk of your bitcoins in an offline system. The hot wallet is online, but has few bitcoins at any given time, and it transfers bitcoins to the cold storage stash whenever it goes over an certain limit. You transfer bitcoins from cold storage to the hot wallet as needed, and at best you'll only lose what's in the hot wallet. There's still the risk that some customers will have to wait for a transfer from cold storage if a lot of them make withdrawals all at once, but it should automate most of the system, at the cost of reduced security.
But you still have to do all this yourself. Even if some company did this as part of their regular operations, they still would be in control of your bitcoins, and it's still a significant security risk.