Best approach to do a website audit?

Screaming Frog's free version crawls up to 500 URLs, which covers most small sites, and PageSpeed Insights is free for the speed side. Then sort whatever you find by how much traffic the affected pages get. Fixing a broken link on a page with zero visits can wait.

The reason every guide says something different is that most of them are written to sell you a 200-point PDF. For a small team, cut it down to what you would actually act on. Crawl the site, then sit with the Pages report in Search Console and work out which URLs Google has decided not to index, and why. That one comparison catches most of it - orphaned pages, redirect chains, thin templates, the lot. Everything after that is titles, internal links and speed, and those are backlog items rather than emergencies. The step people get wrong isn't a technical one: it's auditing everything once a year instead of ten pages a month. A short checklist you actually repeat beats a thorough one you open once.