Were just doing the same kind of thing with our own website.

Make sure you run the existing site through screaming frog and open site explorer. You want to make sure any incoming links are pointing to relevant pages within the new site. there are a number of plugins in wordpress to handle 301's but I usually start by adding them to the htaccess just because it keeps things a bit tidier.

Have you checked webmaster tools to make sure any broken links are addressed?

Also you'll need to add your Google analytics code to the new site. Maybe try Google tag manager if its a new site.