I use brita filter with the jug because the water direct out the tap isn’t very nice. It’s expensive to have to replace the filters though. One last a month or so. You can generic replacements but not looked into it

I use these with a Brita jug https://amzn.eu/d/5XdPAIn

These do a good job mate https://doulton.com/collections/british-berkefeld

I went down that rabbit hole many years ago. If you really want to purify your water (not only form minerals), also from all the pesticides, PFAS, hormones etc... it's an investment...but a really good one...as good water is so important for your health. Of course you could in the meanwhile distill...

Have you asked to an AI?

https://www.h2olabs.com/p-55-stainless-steel-model-300ss-water-distiller-with-glass-carafe.aspx

A great one and easiest to install is Hydroviv. Try it in the US, if you can. I would get a couple of extra filters to switch after a few months, if I were to go abroad. https://www.hydroviv.com/

don't get one of those jugs with a filter. the replacement filters themselves are very expensive. get one with active coal filters directly connected to the tab.