updating website with a new theme

I will start working on a new design for 123ehost.com website.
I will be removing some of the plugins and adding new plugins, but using the same content. What is the best way to go about this? Perhaps setup a new WordPress website at 123ehost.com/new, copy content from 123ehost.com to 123ehost.com/new and then work on the new website with the new theme and then once completed, transfer back to 123ehost.com.

Please advise.