Both Wavefront (.obj) and Autodesk FBX (.fbx) formats are good choices that include textures when exporting.

To export a blender model with textures, you may follow the steps:

In Blender, open the file containing the model that you want to export.

Make sure that all the textures used in the file are packed into the .blend file. You can do this by going to the "File" menu, selecting "External Data", and then selecting "Pack All into .blend".

Select the object or objects that you want to export.

Go to the "File" menu and select "Export".

Choose a file format that supports textures, such as Collada (.dae), Wavefront (.obj), or Autodesk FBX (.fbx).

In the export settings, make sure that the "Selection Only" option is selected.

If the file format supports it, make sure that the "Include Material Textures" or "Embed Textures" option is selected.

Choose a location and file name for the exported file, and click "Export".

It’s important to ensure that the textures are properly assigned to the correct materials and UV maps in the 3D model, especially when you want to import the models into another software application or game engine.

And here are some differences between .obj and .fbx format, that I share in another question, for your references: