There's a cultural component to this as well. In Europe and North America most people prefer 2700-3000K. In Asia 4000K is often preferred.
There are LED bulbs on the market with the ability to change color temperatures. Some people prefer different color temperatures at different times in the day (cooler in the morning, warmer in the evening, for instance) and those bulbs allow that. Also, there is some, not uniformly accepted, evidence that certain color temperatures at certain times in the day might have positive or negative health or behavioral effects.
As far as color rendering is concerned, that's separate from color temperature. You can have a 2700K light source in which many colors look off, and a different 2700K light source in which most colors look great. There aren't good, readily available metrics used for most lighting available. There is a relatively poor metric in common use, Color Rendering Index (CRI), which rates the quality for eight defined color samples against a reference source of light, with 100 as the top of the scale. Incandescent has a CRI of 100. Typical LEDs are around 83, though specialty LEDs go as high as around 98. CRI as a metric is significantly flawed, however, so a higher CRI source can look better for those eight colors than a lower CRI source but worse for general use. If you can it's best to see the actual light source in your target environment and see how it looks to you.
Dimming is another subject. Some LED lights don't support dimming. For those that do, the minimum illumination before flickering or the light turns off completely is a function of both the specific lights and the dimmer. Sometimes manufacturers offer lists of recommended product pairing for best dimming performance but it's not common. Again, unfortunately, you're usually best off trying combinations on your own.
There is yet another light option with dimming. Dim to Warm LED lights lower their color temperature automatically as they are dimmed, similar to incandescent lights. At full brightness they might be 2700K to 3000K and at minimum brightness they might be 1900 to 2200K. This has the "dim to candlelight" effect many people used dimmers to get with incandescent lights.