If I want a complex, yeasty soy sauce, what to look for?
Soy sauce should only contain at most 4 ingredients - soy beans, wheat, salt and water; Chinese ones often leave out the wheat, which is a more typical Japanese ingredient.  The quality of the sauce depends on the fermentation and maturation processes (like a good wine or beer), so is not reliably predictable from the ingredients lists. Some types have sugars and/or spices etc added as well, but it depends on the variant.

Good quality soy sauce is usually expensive, so cost can be an indicator, but is not reliably so, just like you can find good quality cheap wines, you can find good quality cheap soy sauce. In general, a longer fermentation time leads to more varied and richer flavor profile

Dark soy sauces tend to be richer in darker(maltier)/yeastier flavors, while light sauces are saltier with brighter flavors (think aromatics). However, the use of the soy sauce alters how you might interact with it. If, for instance, you were using the sauce for dipping sushi or dumplings, you would use a different sauce to one that you might cook and blend flavors with. Chinese actually have a double pressed variant on light soy sauce used specifically for dipping.

First of all I would suggest working out what you want to do with the sauce, and what style of food you are making - Chinese? Japanese? Thai? Malay? Korean?... etc, all have different ideas on soy sauces and how to use them. Then, go and have a look at the local grocer and see what they have, look for brands that have wine-sized bottles - those are probably the go-to for people doing regular, every-day cooking at home, so will be both cheap and (probably!) moderate quality. If you can find smaller versions of the same brands, they are a good place to start for testing out what you like

Another way to do it is to ask - the people at the shop, your favorite local [insert-asian-food-style-here] waiter, your colleague from work...