How hard is it to move from shared hosting to a dedicated server?

I'm working on a new site with a few people that will be fairly large. Being that it's a new site traffic will be limited initially but we obviously hope it grows rather rapidly.

If we had a ton of cash we'd get a server but we'd rather not do that initially if we can avoid it as the cost would be at least a couple hundred a month.

We're thinking about starting with shared hosting somewhere and then moving to a managed server when it becomes necessary. Is this difficult to do? Will the managed server company typically move the site for you? What's the downtime like in a scenario like this?

Moving to a new server wouldnt be hard if its only a single site. You could simply take the backup of the home directory and the mysql databases and then download the same on the other hosting. Once that is done you could change the nameservers on the domain.

You could hardly expect any downtime

Your new host can do it for you for free or for a small charge. Usually host will do it for free coz they will be getting a good business from you. Hosting website is a long-term association which any host would not like to miss.

If you never done it before it can get pretty tricky, your new host might be able to help you transfer it, they usually do it for free. Good luck!

There is no risk. It's easy. You move the content to the new server and you test it.
Only after that you change the nameserver, and you keep your shared hosting for a couple of weeks after that until the DNS information is updated everywhere.
But it will be hard for your wallet