I find that I learn best by example. Is there a good website or codebase that shows how event handling, collision detection, modeling, and basic 3D drawing works?
The game I'm trying to begin with is a simple racing game where the user controls a small space ship and navigates through channels, asteroid fields, space colonies, and various other obstacles (I know, real original). Movement is in 3 dimensions. The game should know when the shuttle hit an obstacle. There are defined tracks as there are in most racing games (circuits and linear paths).
Pressing the arrow keys should cause the direction vector to rotate appropriately. Also, the ship should use something like an afterburner when the user presses the space bar, for example. Movement up and down is also an option.
Not knowing your initial skill level I suggest you taking a look at Ogre3D. It is a complete 3D-rendering engine that has really clean interface to work with, easy to extend and best of all, it's quite multiplatform working on Windows, Linux and Mac OS X. The examples and tutorials provided are pretty self-explaining.
If you want to write your own OpenGL-only engine completely from scratch, Ogre3D may not be the path to follow...