In addition to setting up 301 redirects as @swilliam mentioned, I would keep the same keyword density in content, headings, meta + URLs. The order / layout can change, but the density shouldn’t.
Don’t expect a migration that keeps your rankings intact, they could easily drop 1-2 spots - but if done right, you’d quickly gain them back.
so you are talking about on-stie SEO, correct? This means I should ensure that the images have alt tags and that the pages have nice titles etc…any other details I am missing? And this means that the off-site SEO is already in place and should not change?