How to read the result
A redirect sends a visitor from one address to another. Each step on the way is a hop, and each hop answers with a status code. 301 and 308 mean the page moved for good, so search engines move the old address's place in results to the new one. 302 and 307 mean the move is temporary, so search engines keep the old address. 200 is the page itself, loading normally.
One permanent redirect straight to a working page is what you want. A chain, two or more hops, slows the page down and wastes crawling: point the first address straight at the final one. A loop sends visitors round in a circle and the page never loads. A redirect that ends on a 404 leads nowhere: point it at the closest live page instead.
When to check your redirects
After any change of address: a renamed page, a move to HTTPS, a new domain or a redesign. Paste the old addresses in the list view and check that each one reaches the right page in one hop. Then update your own links and your XML sitemap to use the new addresses directly.