Migrating servers, themes from non-Revolution to Revolution

[Tannerman]

This may seem like a rather simple question, but after searching, just wanted a little clarification.

I currently have a WP-powered beverage review website (BevReview.com) that is hosted on a budget host and a freebie WP theme. Due to a (thankful) increase in traffic, it's outgrown its current home, and I'd like to migrate it to a reseller server account that I have other web projects sitting on.

What I'd like to do is also work on a redesign at the same time using a Revolution/StudioPress theme. I'm kinda wondering what the best process should be to accomplish this. Ideally, it would be great to work on a WordPress install on the new server location and work with the new theme there. Then, when everything is ready, move over the content from the old server to the new (I assume by copying databases and whatnot) and then changing the DNS on the domain name.

Is there a tutorial out there for this such a thing? Do I go ahead and basically install a fresh copy of WP on the new location and then port the info over from the old WP install? Or is there a different methodology involved? I'm more of a project manager/copywriter Web guy vs. a server person, so this stuff is rather confusing for me.

Any direction you could provide would be appreciated.

Thanks,
Steve