i am interested in implementing a simple old-school 3d game very much like DOOM ( in c/c++ ). what 3d graphics engines do folks recommend? should i just create it from scratch with opengl? also, it's very important that the package handle mirrors and reflections properly. thanks!

OpenGL can do all of that and more pretty easily.
And dont forget, DOOM is not a 3D game, its 2D
with some tricks to make it appear like 3D.
It is actually quite limited, like no ramps, no vertical aim,
no real floors or ceilings, no over and under rooms...
And the monsters were not 3D meshes but instead 2D sprites.
You can get the doom source and have a look for yourself.
They had to make do with what processor speed was available.
Nowadays things can be much more complex and run at good rate.
If your interested in 3D game engines, look at Quake sources.
Theres plenty to learn, and much discussion about implementation.