I know of two that import OBJ's with textures...
The Fluid importer is fastest, but costs a few $.
My older/slower OBJ-importer is 'free' [you can of course donate!].
There are a few others - I think they only bring in geometry ?
An OBJ file that has materials associated with it almost always ships with an MTL file.
This defines the materials.
It is almost always expected to be in the same folder as the OBJ.
To check this read the OBJ in a plain-text editor - near the start it usually sets up the MTL file.
Assuming you have an MTL file associated properly with the OBJ...
That defines the materials' colors.
You can also read that in a plain-text editor.
If a material has an associated texture, then the path to its image-file is specified in the MTL code.
Usually these image-files reside in a named subfolder, which is given in the path for each material.
Occasionally a 'non-standard' MTL expects its image-files to be in the same folder as the MTL itself.
Read your OBJ...
Find the associated MTL.
Ensure it's in the correct place when importing the OBJ.
Read the MTL and ensure any needed image-files are also in the correct folder or subfolder...
Once it's set up right, then any importer which respects materials should work...