I think you’re being wise in considering the options before diving into the project.
You’ll want to look at this:
http://modxcms.com/moving-sites-to-new-servers.html. It’s based on the concept of developing locally and then moving the site to a remote server.
As for the redesign, it depends, first, on whether the old site is a MODx site. I’m assuming no, since we’re in MODx 101

.
In that case you can either:
1. Port the site to MODx and then redesign it.
2. Redesign it first and then port it to MODx.
3. Just build it from scratch in MODx.
That decision would probably depend on how major the re-design is and how much time you have.
I would most likely install MODx locally, then build it from scratch with some cutting and pasting of content you want to keep, then copy it to the remote. Some people recommend installing the MODx demo site -- if you do that, I’d recommend making that a separate MODx install so you can just use it for reference and ideas on how to do things.
I’m curious to see what others have to say on this topic.