I may as well say something about a pet peeve of mine. Sometimes when you look at a website's source code the first page before scrolling down is full of included CSS and JS files. What on earth for? Do people really need to load everything on every page? Perhaps they do, but for myself I won't load the libraries for FancyBox, Google Charts, Prism or anything else I use unless the page actually uses them. The files themselves may be tiny, perhaps even just a few kilobytes, but they use resources.
The idea behind all of these utilities is to provide a page free of errors and load it as fast as it can be into the browser. I'm not even sure if it is possible to optimize a website or page to pass every test, but these point out the major bottlenecks. Here's some of the tools I use:
Accessibility - The W3C page Web Accessibility Evaluation Tools List has 160 validators. I haven't yet made up my mind which ones I prefer to use.
CSS - I use the W3C CSS Validation Service to check I haven't made any dumb mistakes in the site's CSS file. The W3C Nu HTML Checker can also check CSS files. I minimize it using Minify which can also handle JS files.
Editor - I've been using Adobe DreamWeaver to edit the pages for several years. The HTML hints are great. The only downside to the program is the spell checking. Every other editor has automatic spell checking, DreamWeaver never has and it is annoying. Everyone makes mistakes spelling at some time or another and it would be nice if checking was done as you type.
Images - Apart from video, images are the largest content of most websites. I optimize the images I use in Adobe Photoshop, but Cloudinary Website Speed Test is optimized to show which images are slowing your website down.
Minification - This is the process of removing all white space and line breaks from files. It reduces the file size without more agressive compression. I use Minify which can handle both CSS and JS files. I should add that I run my own Apache webserver, the "Server in the Cellar", and that has the gzip deflate option turned on.
Page Loading Times - Some tests measure everything about a page and gives results on an analysis of the whole thing. Solarwinds Pingdom is one such, others I use are Catchpoint Web Page Test, and of course Google PageSpeed. I should add that I run my own Apache webserver, the "Server in the Cellar", and that has the gzip deflate option turned on.
Server - As I run my own Apache webserver, the "Server in the Cellar", I'm interested in tools that can help optimize and protect it. Some of the better ones I've found are Detectify, this company once offered free scans for a sinle site. I started using it and they still scan it, even though the offer was withdrawn years ago. Immuniweb Website Security Test, Ionos Website Checker, Mozilla Observatory, Pentest-Tools Website Vulnerability Scanner.