It all depends on what your subject is and the conditions you're in. No two rooms are ever alike and inanimate objects always stay still, people do not
IS helps with your movement at slow shutter speeds, but it doesn't stop subject motion. The majority of digital slrs do not have inbuilt image stabilization. You may have it in your camera, but if not you'll need lenses with IS built in (if you have a dslr of course).
I myself have always gone for lenses that give faster shutter speeds. They suite my style of photography they suite the conditions i shoot in and the subjects i shoot. You have to figure out what you want to do so that you can then make the right choice based on your needs. There's also tripods which are fine for static subjects in tough light, but will be no more help for freezing subjects then IS is. You really do need to understand the environment you're in so that you can shoot in it successfully
Noise
It's a part of digital photography just as much as grain is in film. You get film speeds from ASA 50 to 3200 the higher the number the more grain. The higher the ISO the more noise but it means more light and there are times when you're going to need more light. I would not threat about it too much it can actually add to a shot if it's the right one and there is plenty of software to reduce it such as the one Bill spoke of.
It all depends on the light you have to work with. Even when i have a lens wide open at F/1.4 with an ISO of 3200 i can still find myself with a shutter of just 1/30 sec. You do what it takes to get the shot; Noise/grain and shallow depth of field becomes just a signature of of what it took to get the shot.
If that's all greek to you, then you need to learn how aperture/shutter/ISO relate to each other.
http://www.dpreview.com/learn/?/Glossar ... ure_01.htm
http://www.dpreview.com/learn/?/Glossar ... eed_01.htm
http://www.dpreview.com/learn/?/Glossar ... ity_01.htm
All of those relate to exposure
http://www.dpreview.com/learn/?/Glossar ... ure_01.htm
What uses having a great depth of field, if there is not an adequate depth of feeling? -
W. Eugene Smith