Restoring the last texture state in legacy OpenGL 1.x

Question

I would like to remember a current texture state in OpenGL 1.x and later restore it. I can use glIsEnabled to check which texture types are active.

1. Does it make sense to have enabled more than one text type, for example, GL_TEXTURE_2D and GL_TEXTURE_CUBE_MAP?

glGet* function allows to get a current texture id, for example, GL_TEXTURE_BINDING_2D but to bind previous texture I also need to know appropriate target for glBindTexture.

2. How to achieve it?