How to approach the problem

I’d like to write a simple (as I understand it for now) program for displaying 3d objects (each comprising of lines exclusively, no textures, surfaces etc.). It has to allow me to manipulate the view by mouse (rotate around particular point in space, zoom, translate) and have an option to manipulate all the objects as well as every object independently.

Now, being totally new to OpenGL programming, how to approach that? My main concern is how to learn OpenGL philosophy to get the thing done? Should I comprehend all the superbibles and do all the algebra by hand or are there some feasible shortcuts/helper functions in OpenGL? If you could hint just some keywords I could explore myself.