How do I manage a list of texture objects with instantaneous lookup when I need it

I have a function that loads a bitmap from a filename, generates a unique texture ID, and returns it.  In an application where I could possibly need hundreds of textures my current setup simply will not do, or it may, and that is my question.

We are to assume that the game logic or game engine itself will demand a list of objects for whatever game we're playing.
Then we can assume that each object initialized in the engine will need to acquire various resources, textures perhaps.

Should the objects call the loadtexture function?
Should the engine call loadtexture for each object loaded?
Should the engine wait for a list of objects to be initialized, use that information, and load everything in one foul swoop with a modified loadtexture function.

I think that the engine could better manage this responsibility because it is aware of which objects and resources are currently loaded.

I have a resource manager, that is essentially a map wrapper that ties Data<T_> with a string or integer.
The engine would register each object and as it would do that it would make calls to the resource manager to check if the filename has been loaded into the manager.  If the filename has been loaded it will return a reference to a texture id, if the filename has not been loaded it will run loadtexture on the file name and return the id.

I guess there are multiple ways to achieve what I'm trying and I'm just wondering what you all think is the best way.

Lets assume we want to precache some of the objects.

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int LoadTextures( const char *filename )			// Load Bitmaps And Convert To Textures
{
	Bitmap image;									// Create Storage Space For The Textures
	image.Load(filename);
	GLuint texture = 0;								// Texture ID's
 
	// Load The Bitmap, Check For Errors, If Bitmap's Not Found Quit
	if ( image.GetImg() != NULL )		// If Texture Image Exists
	{
		glGenTextures(1, &texture);						// Create The Texture
 
		// Typical Texture Generation Using Data From The Bitmap
		glBindTexture(GL_TEXTURE_2D, texture);
		glTexImage2D(GL_TEXTURE_2D, 0, 3, image.GetWidth(), image.GetHeight(), 0, GL_RGB, GL_UNSIGNED_BYTE, image.GetImg());
		glTexParameteri(GL_TEXTURE_2D,GL_TEXTURE_MIN_FILTER,GL_LINEAR);
		glTexParameteri(GL_TEXTURE_2D,GL_TEXTURE_MAG_FILTER,GL_LINEAR);
	}
 
	return texture;							
}