You posted several months ago, maybe you already have an answer but I hope to be usefull to anyone who gets here
Well, I started with Bullet some time ago, and so far, the Demos of bullet that comes with the installation package are very usefull. But it takes some work to extract the lines of code that you really need (at least for me, I'm a beginner programer).
There are a few Bullet tutorials, about Bullet and its integration with some 3D application (Blender, Ogre3D, etc), but I havent see a "just Bullet" tutorial.
There is a book called "Bounce, Tumble, and Splash!: Simulating the Physical World with Blender 3D" available on Amazon. I havent read it, but looks interesting.
System requirements: I dont know :S... I didnt see anything about that in the Bullet SDK Manual, but I think you should be able to run it in most of the computers that are still operational today. Maybe you should see the requirements for the 3D software you will use instead.
NOTE: I had problems trying to install Bullet in Linux Ubuntu 64-bits. I solved It deleting some Demos in the makefile before building the package.
Bullet Demos comes with GLUT, an OpenGL based 3D library... you can start using them, but I think there are better options like Ogre3D and OpenScenGraph.
Maya or Blender? (I'm not familiar with Houdini)
I havent integrated Bullet to any of this tools, and I have not the right to tell you what is the best, but I did use both, and seems to me that Maya is a lot easier to learn and use than Blender, anyway, Blender is a powerfull 3D modelling tool, and used for game development also. The book I mentioned before, is about integrating Blender and Bullet.