When creating a new DaVinci Resolve project, I think it would be better to specify DaVinci YRGB Color Managed for the color science in the color management of the project settings, and specify DaVinci Wide Gamut in the Resolve color management preset. But when do you have to make other choices?
Presets are just presets, basically choosing the largest possible color space to export in the future. DaVinci Wide Gamut is a large color space, so it covers all color spaces, but if you don't need that wide color space, you may choose other options.
Non-Log materials can have various color spaces, but Rec.709 Gamma 2.4 is common for now. This is a so-called "video" image with contrasting colors and brightness.
Color management and LUTs are similar in principle. A conversion from one color space to another. So basically you don't need to use LUTs when using color management. Of course there are exceptions.