Before directly starting with your re-design process, you need to check out the following list :
(1) Missing page titles.
(2) Duplicate page titles.
(3) Broken links.
(4) Duplicate H1 tags, Missing H1 tags.
(5) Missing Meta description.
Also check manually :
(1) XML sitemap
(2) Robots.txt
(3) URL structure
(4) Pages indexed by search engines.
(5) Site speed and performance.
After this, you can work on your landing pages, check for the navigations and use some fresh color-mix.