Can I choose a new template and keep the old website up and running before I publish the new site?

We have changed our website so much that I think it would be easier to start over with a fresh template. Does my current design stay up and running for the public to see until I publish the new design? Or once I choose to select a new template does everything public get deleted?

Also, a lot of websites, especially news related sites have top stories that flip from one picture to the next, is there any way to do that without using the image scroller? Some of the features on homestead look "cheap". I'm looking to make my website more professional looking instead of so "cut and paste".