To preserve rankings after a permanent page move or site redesign, always use a 301 redirect. This tells Google et al that the page has permanently moved. Most, but not all, of the link power associated with the old URL will transfer to the new one.
For redirection, I've used a plugin called simply "Redirection" with good results (author is John Godley). It provides quite a bit of flexibility in creating redirects and also tracks 404s. But, my choice wasn't a result of careful study - there may be other good ones out there.
You can also set up redirects yourself directly in the .htaccess file, but the plugin approach is a little easier.