Should I create a component to wrap each mesh, texture, animation class
and wrap the rendering loop as a system in my framework?
No, you should definitely not create a component (in the "entity-component" sense) for each of meshes, textures, animations, et cetera. What good is a texture component attached to an entity without any of the other rendering components? You'd just be creating abstraction, overhead and complexity for no reason.
What should I do?
Don't think too hard about it. It's not magic.
Entirely independent of your entity/component system, your rendering system should be able to take a description of a rendering task and queue that task for rendering. A "rendering task" is fundamentally just a structure containing a mesh reference, texture references, shader references and shader constant information, animation references, and transformation information; one structure containing everything necessary to "draw something." Major existing rendering engines provide this functionality in one form or another.
To tie your rendering system into your entity system, create one component type which simply acts as a "visual" or "portrayal" component. This component simply holds the rendering description for that entity, and provides access to it so it can be manipulated or updated or whatever.
The processor associated with these visual components simply collects them all and hands them off to the real renderer, which can batch or sort them as needed and do the actual rendering.