Tile choice - how/where to start?

The quality depends on the room and can be recognized by specifications of various parameters, both for a tile and for a carpet.

which would be?

I have the following quality criteria (layman)

[*]Frequently repeating patterns are out. Of course, it’s cheaper to use a smaller printing template, but I don’t like to see duplications.
[*]Backing material: For floor tiles, I make sure that the backing material is porcelain stoneware and matches the color of the surface so that any chips later on are less noticeable.
[*]Chips: I look at several samples. If they are all damaged, that’s a bad sign.
[*]For "special tiles," the appearance is a direct quality criterion. Moroccan wall tiles can look dull or brilliant. The same goes for mosaics, especially glass mosaics, which can be either dull or sparkling. The differences are enormous and are reflected in huge price differences here. Hand-painted ones are also, like in art, qualitatively easy to distinguish.
[*]Depending on the intended use, properties such as slip resistance or abrasion resistance play a role, but I would not consider these primary quality criteria.

Aside from the "special tiles," I think a high-quality tile doesn’t have to be expensive. Strangely, the particularly beautiful ones are rarely the cheaper ones after all.

which would be?

For example abrasion, as already mentioned: don’t take any in the hallway that are only suitable for the bathroom. There are values... numbers... you have to check yourself, I’ve been out of it for 5 years.
Do not use smooth wall tiles on wet floors -> slip resistance, also mentioned by . Point 1 from ... for me also the reason for warping, calibration...
Personally, I would always choose something off the mainstream.
Overall, Google already gives you optimal background knowledge.

I would personally always choose something away from the mainstream.

We thought the same and then found wonderful tiles on a sample area in a Hagebaumarkt. They are now in the middle part of the building.

We thought so too, and then we found wonderful tiles on a sample area in a Hagebaumarkt. They are now installed in the middle part of the building.

Just because they were lying around in Hagebaumarkt doesn’t mean they have to be mainstream. A colleague bought a great tile for the kitchen at Bauhaus. Most people probably would have turned up their noses five years ago when he bought it. It is colorfully patterned and glazed. It looks amazing as stripes in front of the kitchen unit. In our area, for about 6.8 years now, almost only anthracite is laid on bathroom and kitchen floors. In new houses with condominiums, 99% – I’m putting my neck on the line here.

You are right. I wanted to say that you can find good tiles not only at the "expensive" stores.