We're doing a top-down redesign of an existing website. Since there a number of years of great data we do not want to lose, should we remain within the same Property, move to a new one, or create a new profile within the same property?
Any help would be appreciated!
Use the same property as the old website and create an annotation for when you launch the new site. While you're in there, I'd create a new Universal Analytics property. Universal Analytucs is still in beta, but it's going to replace Google Analytics so you could get familiar with it by dual-tagging your website - https://support.google.com/analytics/answer/2817075?hl=en
If you're really feeling adventurous, you can check out Google Tag Manager to manage both your Google Analytics and Universal Analytics implementations - http://www.google.com/tagmanager/