The earlier you set up your own servers and take care of them the better you'll be at it. If your seriously strapped for time maybe you can put it off, but it's a skill you want to have.
Shared services mean that mistakes made by any other client on that machine are very likely to damage you. Also, without root access, you are often stuck not being able to set a configuration well. For a hobby site, or a sandbox, shared hosts are fine and cheap. I would never deploy a real web application on one though. Many places will sell you a Xen VPS slice for $20-30/mo.
What you trade off in control you make up for in free time. Granted, as you get larger and develop traffic, the trade off will need to be re-evaluated, but I don't see any major benefits at the beginning.