For me personally, Google PageSpeed Insights is a pretty good tool for what it does. However, it’s worth remembering that it generally runs off of servers in datacentres with massive pipe connections at 10GB/s and beyond, which is far beyond what users will ever have access to.
For more real world testing, I tend to use Lighthouse, which is integrated within Chrome DevTools. It does pretty much everything PageSpeed can do - including generating a PageSpeed report - but it also does a few more magic tricks that can’t be done via a server based tool. It also gives me results based on a real world internet connection (which is very real world for me, because I’ve only got 8 meg down, 2 meg up!).
I also have access to Google Search Console and Bing Webmaster Tools for domains/sites I own or manage myself. Bing Webmaster Tools is pretty terrible and tells me practically nothing useful, but Google Search Console often flags up very useful advice - such as issues that can destroy SEO. It also offers a way to have Google re-check pages after you fix them and have them re-processed. If your fix works and Google verifies the fix, the alert is cleared from your dashboard and GoogleBot will take care of the rest on its next run.
However, low scores are something to be aware of regardless. You ideally want to be turning both PageSpeed Insights and Lighthouse green where possible, while also keeping Google Search Console etc happy. There’s other similar testing tools as well of course, some of which can do real-world simulations. I know a few, but I need permission to mention them here.
While my own sites consistently hit the high 90’s for Desktop and high 80’s to low 90’s for Mobile, that’s mainly because of things I do which are otherwise pretty difficult to pull off. Aim for the green zone and that’s a great step already. :)