Chemically, inks are different from paints. They are far, far more highly pigmented than paints, and as Dustin09 says, more transparent. It all depends on what you want to use inks for - for a wash? If so, you can use just Badab Black straight from the pot. Or if you haven't got it, dilute some black paint down, add some matt medium, and you're pretty much done converting it to a rough wash.
A similar process applies if you're trying to make a glaze, except that I would even dilute pure Badab Black before using it for glazing.
Otherwise, if you're just using a black colour to darken a colour, then either Badab Black or just black paint will do. Some context as to which articles you're looking at will help us readers give you a more precise answer.
For ink brands, just use whatever suits your purpose. GW inks are great for using out the pot, although they're pricey for the volume you get. Vallejo gives better value for money, and I find the coverage comparable to the GW stuff. I have never used any other inks of any other brands, although I've heard some good things about P3 inks.
Personally, I don't really bother with inks nowadays, unless it's for a glaze. The higher pigmentation seems to work better for me in glazing. I just use diluted paint most of the time.
