Thanks for the replies, but I seem to be getting answers to slightly different questions, probably because I was a bit brief earlier.
And I guess I should start with a little introduction.
I have been doing Java programming for about 15 years by now. Mostly desktop GUI and some math and graph things. I hope that I would not need to go very deep into the OpenGL at least not before I am more familiar with 3D. I have some experience in trying to keep things as trivial as possible without breaking the purpose of it.
The whole idea of doing a roguelike randomly generated dungeon crawler comes from my recent successful attempt to make a little fitness game prototype with OpenCV (OpenCV JavaCV racket game (hello world) - YouTube), but the first problem is that the game is boring like hell and the second problem is that although it successfully provokes hand movements with large amplitude there is very little fitness effect unless the legs are also involved. The boredom problem might be solved by doing a different kind of game, and the legs problem might be solved by involving leg gestures for navigating a dungeon.
Complicated 3D models (like epic spiky armor) are not really mandatory in roguelikes, the graphics can be more symbolic rather than detailed. That might enable me to concentrate more on the gameplay, especially considering that it will probably be a solo project for quite a while and I am new to 3D. I am not intending to have the most awesome 3D graphics ever seen in the world. I just hope it would turn out simple to look at and somewhat immersive.
I mean, it might look something like this:

My intention is to avoid long straight tunnels and wide open spaces in general, to limit the field of view. Cast shadows would be important because I would appreciate giving the player a hint about a monster around the corner if monsters emit a little light, but without light shining through walls.
What makes jMonkey rendering considerably faster or slower? Cast shadows, especially with multiple light sources? I could perhaps find a workaround for the lighting, if that would be a serious issue. Would there be considerably lower requirements without bump and UV maps?
Is rendering 3 times per frame (to get the half-panorama like this post with a screenshot) considerably resource intensive? I don’t want the player to flap legs about every time he wants to look slightly left and right to see what he would normally see with human ~160 degrees vision. The curved wall in the mockup image is not really curved, it is a side effect of the panoramic projection.
Computer vision also demands that the player is not looking at the screen from a very close distance like sitting by the computer, so the screen would need to be larger like 20’’ but lower resolution would be OK for the same reasons.
There is more, but the post looks like a wall of text already, and the rest is not even remotely relevant to the system requirements.
This particular thing I am trying to make would be the highest requirement thing on my computer because I am currently not using it to play games and not intending to use it for playing sitting-by-the-computer games in the future. Right now my computer is from year 2003 and it is OK for running Eclipse IDE, GIMP, and video tutorials and demos on YouTube etc.
So the main question would be: what would be the LEAST capable computer that you would expect to probably run this game smoothly? Not about what graphics card a “generic sane person” would buy.
The reason I would hope for an answer somewhat relative to General System Requirements for Applications Built with jMonkeyEngine is that then I could go to shop and say “I would like something that is about X better than those requirements on that web page.”