What's the best way to choose texture resolution for your 3D models?

texture resolution is a very strange, interesting topic. What's already been said is true for the concept of PPI, but I think it's worth considering that high-res textures don't always have to be seen as resource heavy. Let's put it this way. You've got a challenge for your player: There's a room with 12 cups. 11 are evil, 1 is holy (Of course you want the holy one!). Regardless, all 12 have details that tell you if it's bad or good. Instead of assuming each will have it's own set of 512 textures (since 512 is less than 2048), you could have all 12 fit within 1 UV map, and allow each to have their texture come from 1 single x2048 texture. 2048 is bigger, but it ultimately means you'll have just 3-4 large textures, versus 36-48 x512 ones!

Although there is another factor we need to pay attention with it and affect strongly in the quality of the texture beside the resolution which is the actual scale of a map for example if we have a 2k or 4k texture map we must be sure that it has a proper scale or dimension in real life because if it's a 10 cm sq map that will cause a non-realistic repetitive pattern so we have to make sure that our texture is not a small piece of wood or any other material. So resolution and scale of texture have same importance.

I tend to follow a very simple alogorthm for choosing the right resolution for textures. If the objects is far from the camera and occupies a small percentage of the shot, then you can use smaller resolution textures and vice versa.

Based on the final image render if the image is 2K render so the closest textures to the camera can't be less than 2K, maybe the far textures can be 1K

It really does depend on what exactly I'm attempting to texture. Like a lot of others have said, your texture resolutions should really depend on the importance and distance of the object having materials applied to it. Are you creating an asset that will most likely be seen at many different distances? Maybe it's worth creating several different resolutions of texture, and base those on distance from camera. These are of course known universally as LODs! (Level of Detail). Your tree may very well want to use 2k or 4k resolution textures when you're right next to it; meanwhile, if you're so far away you can barely see it, perhaps you forego even a textured model, and create just 1 simple tree texture. Nobody's gonna notice if done right!

Texture atlases are truly the way to go here. They do certainly have some limitations when it comes to visual fidelity, but that's not the rule. I find atlases truly shine when you have a lot of different elements that will be drawing on the same basic textures. Ever looked at an old PS1 game like Silent Hill? Those games were often on a grid system, and had a single image containing upwards of 10-20+ textures on it (like road, sidewalk, grass, dirt, sewer drains, etc). Every single tile of this texture could draw on this one single image, effectively texturing a vast majority of your game with literally one single image file.

There's so many resources out there nowadays to learn what the best approach is based on your needs/project. Youtube channels like BlenderGuru have insanely high quality tutorials/advice on what the best approach is for each situation. Are you texturing a massive landscape? Baked textures may not be the way to go. Instead, you get a seamless series of PBR textures which can be tiled infinitely, while still maintaining the crisp detail you're looking for. For other objects you'll inspect closely (let's say a sword that can be seen in the player inventory), you very likely want to bake your textures. This itself is a very expansive discipline, but it makes a difference. "How to create and bake textures for games"; that's your Google search!

I've learned that while there are standards, there's also no 'right' way to approach texturing when you're in the learning process. Allow yourself to do things inefficiently, or wrong, since this will inevitably open the path towards researching and discovering a better way. Maybe your game is textured inefficiently. That's okay! Because on your next project, you'll know what you did poorly, and approach it with an improved process from what you gained from educational resources online, as well as your own experience. There's such an overwhelming sense of doing it correctly, or the 'right' way from the get-go. But remember this: if you always did things the 'right' way without ever doing something wrong, you'd never learn how to improve!