Sounds like storage and throughput are your main concerns. I checked out your web site, and it doesn't appear you would need any other resources besides storage and throughput.
I don't think you get better throughput with VPS vs Shared plans and Shared plans offer unlimited storage.
The shared plan = 2,000 Mbit Connectivity (Although this is likely a shared amount, so at peak hours this is probably much less )
The VPS plan = 100 Mbit Connectivity
Unsure about Dedicated...
The advantage that most users seek when upgrading to VPS from a shared server is the "dedicated/allocated" processor/memory resources and more flexible server configurations. If you are running scripts that take lots of processor power or memory, eventually they'll kick you off the shared servers.
If shared server admins aren't telling you that your site it using too many resources, and if you don't know why or how you could take advantage of the VPS plan's ability to configure your server, than I suggest you stick with the shared plan.
Also, remember your connection to the Internet and the experience you receive is often highly dependent on your ISP and the traffic on the Internet in general. Even though you have a broadband connection, you might get less than optimal throughput during peak usage times.