Help: Starting fresh with WP while still maintaining the current [non-WP] site?

Apologies if this has been asked before, I tried searching for my answers to no avail.

Anyway,
I work for a small web store which has been running MivaMerchant with a domain from GoDaddy. I’ve convinced my boss that WordPress would be a simpler and more cost-effective option, but now that we’re going through with it, I’m stuck and don’t know what to do.

I need to begin designing and testing a new site using WordPress and WordPress plug-ins but [as far as I know] I can’t do that with the current domain if I want to keep the store online. We have another domain that isn’t in use at the moment, so I’m thinking I begin there and transfer everything over once I’m finished. [so the switch is as seamless as possible]

Here’s the problem; I’ve never done this before, and I have no experience with www.remarpro.com- only wordpress.com. I know I’m capable enough to get the job done, but I know it’s going to be a bit more complicated than just switching everything over.

So; My questions:

-Is designing the site on a separate domain the best way to go?
-Where do I begin? [as far as setting myself up]
-I already have some in mind, but which plug-ins would you suggest?

-How do I go about transferring the finished product to the old site?
-It can’t be as simple as removing the old miva file/folder structure and transplanting the new WP one via Filezilla, can it?

I realize it’s probably a lot to answer, but your help would be greatly appreciated!

Thanks,
Patrick