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There's really no "right" answer for this since I don't recall any official statement about it. I would just move, make sure all my redirects/content are done. Then start applying the redesign. Normally I would wait for it to be crawled but nowadays, I just jump right into the redesign after moving all the content/301's. I've never really seen big problems, normally, just small dips but it usually goes back to normal.

As I said before, if you are changing just the domain, then you can do the whole site in one redirect, but if you have a different page structure and thousands of pages, it would be a waste of time to do any pages that does not have a external link.

Hi Matt, In general, my advice would be to achieve permanent 301 redirects at as granular a page/folder level as possible (prioritized by the current number of linking root domains - Open Site Explorer's Top Pages report is a great tool for this). Where the rebranding & migration is concerned, I would strongly recommend reading through two resources here at Moz:   Ruth Burr's overview of Moz's own fairly recent move (from SEOmoz.org to Moz.com) and Aleyda Solis's handy "Achieving an SEO-Friendly Domain Migration" infographic Between both, I think you'll have your bases covered. Best, Mike