I'm starting a hobby game project on Windows that will make heavy use of 3D graphics effects. It will most likely be written in C++.
Should I use OpenGL or Direct3D for my graphics backend? Why?
Or should I use a ready-made graphics engine such as OGRE 3D? Which one?
Some "how to get started" links would be useful. (On either technology, or both.)
Edit - Yes I really meant Direct3D, not DirectX, thanks to graham.reeds for clarification
Edit - Mihai Lazar pointed out that I could also use a graphics engine such OGRE 3D. Edited the question to reflect this alternative.
Best thing to do would be to abstract over your renderer as much as possible, to make porting to the other technology as painless as possible.
The suggestions for abstraction of an engine are good, assuming that you know what you are doing. It's difficult to write a good abstraction layer for graphics without having done it already.
I would suggest that you just pick one. You will pick up the concepts from either easily enough -- enough so that you can potentially work on an abstraction layer, or the other library easy enough. But just do it. I really wouldn't worry so much about which is the right one. They are both good, solid performers. DX10 (if you have Vista) may have the slight advantage of more up to date shader models, but for someone starting now, that is pretty irrelevant I think. GL has the advantage that some of the nigglier matrix/vector math operations are either hidden from you, or provided for you (although I think DX has some of these as well.)
While OpenGL is by far easy to start with and as some people already wrote - getting a triangle to show on screen and from there move to textures, particles and more can be done within a day.
I do however think that a good question to ask is what is your final goal.
If it is a simple game, no skeletal animation, and simple 3D - OpenGL is definitely the answer. If you aim way higher and don't want to put the time in developing all the technology from scratch (or go hunting for free libraries and putting all together) then DX is a good choice, I would go for DX9c until DX11 comes out.
If you don't mind messing with other languages other than C++ you should also take a look at the XNA development environment - it became quite mature and good.
Just as well, using an already existing engine is good if you know that it'll give you most of what you need, for the right price and will save you the time to develop it yourself, the main problem is that you'd need to go over several game engines (Ogre, Game Studio, Torque, etc..) and then make your choice based on limited experience - read as many reviews from casual developers as you can before you proceed, and try to take a look at the code if you intend to change it.
Hope it helped.
Start with OpenGL because there are good textbooks and other online references on it. Once you get the hang of writing 3D game, you would be able to make the judgment for yourself.
Finishing a game, even if it's really stupid and simple just to get you going, is more important than picking the right library. With glut, you can get some 3D object to show up on your screen in a day. Start with NeHe's tutorials.
I did my dissertation at uni on a comparison of OpenGL vs Direct3D. The real benefits of Direct3D are that it has a regular release schedule - it's always being updated to take advantage of the latest advances in graphics hardware. How long has it taken between the OpenGL 2.0 and 3.0 releases? Also, a lot of work has been done in extensions for OpenGL, which means only some rendering will work on some cards.
Having said that, OpenGL will be easier to start programming with. As Direct3D is based heavily in COM, it has a steep learning curve.
If it were me, I would be choosing DirectX over OpenGL. That's at the cost of non-platform independance.
My opinion is that OpenGL is best.
OpenGL SuperBible: Comprehensive Tutorial and Reference is a good reference.