Best approach to fix broken links?

Crawl the site first (Screaming Frog's free version does 500 URLs) so you have the full list, then sort them into two piles. Internal links pointing at dead pages: edit the link to point at the right page. Don't just redirect, fix the link itself. Dead pages that other sites link to: 301 them to the closest relevant page. Search Console shows which pages have external links. And don't redirect everything to the homepage. Google tends to treat that as a soft 404 anyway.