An ND filter will reduce the amount of light into the camera without introducing a colour cast - this allows for longer shutter speeds (for running water etc) or wider apertures (for shallow DoF) in a given light. For what you're wanting to do they may not be necessary, it depends on the ambient lighting.
First off you're looking to set your camera to the lowest possible ISO and narrowest aperture (max f number) that'll give you an idea of the longest shutter speed available for the current lighting. For running water it doesn't need to be forever - 1/2s upwards will blur the water enough so filters may not be necessary. Obviously a tripod is essential.
In terms of brands there are plenty out there, I use Cokin square ones as I can use the filters on different lenses. They're OK, not wonderful quality and a bit delicate. Screw in ones are a bit less versatile but optically they tend to be a bit better - Hoya is a decent blend of price and quality. In either style I would go with a 1 stop and a 2 stop filter, that gives you flexibility along with the ability to stack them to give a 3 stop filter