Free tools are enough to start: Search Console for indexing and queries, a crawler (Screaming Frog does 500 urls free), and PageSpeed Insights on the slow pages. Don't audit every page either. Check one of each template - a fault in the product template is a fault on every product.
Do it in that order and don't skip ahead. First, can Google reach and index the pages that matter - crawl the site, then compare what's indexed against what should be. Half the audits I've picked up stop being interesting the moment you find a whole section blocked or noindexed by accident. Second, the technical basics: broken links, redirect chains, duplicate versions of the same page, anything painfully slow. Third, the pages themselves - does each one have a clear subject, is it actually answering the query, are there ten thin pages that should be one good one. Links last. The mistake is opening a tool, exporting 200 issues and working top to bottom, because that list is sorted by what's easy to detect, not by what's costing you traffic.