There seem to be as many inks as there are nibs and surfaces to write on. Since you are just starting out, purchase a bottle of ink made for dip pens when you get your pen. You'll be fine purchasing a simple calligraphy set that already includes several nib styles and inks. Otherwise, Higgins Eternal Ink is the black ink of choice for many calligraphers.
Ink choice depends on the pen type. Use ink formulated for the pen, whether dip pen, fountain pen, or other pen. For fountain pens, only use ink for fountain pens; other inks or paints may be too thick and will clog up the pen.
We have several methods for loading ink onto the dip pen. We can dip the pen directly into the ink bottle (keeping the bottle at the same side of the work as the hand that holds the pen), wipe it on the bottle, test it on a test page for flow, then start inking. Or we can keep the bottle of ink on the opposite side than the ink hand, with the non-ink hand holding a soft brush. We dip the brush into the ink bottle, then brush the nib to load it. We keep the brush in hand, ready to load again. This method is often used when the calligrapher wants to mix colors.
If you expect to work for several hours at a time, do not leave the ink bottle uncovered or it will evaporate, leaving too much sediment. Instead, pour some of the ink into a smaller vessel for use ("decanter"), and cover the original bottle. Cap the smaller vessel if it won't be used for a long period.
If you will lay your pen aside for a while and take it up again later during a long session, have a small vessel of water nearby to dip the pen so the ink won't dry in the pen.
Ink flows because of gravity. If you find the ink flowing too readily from the pen, then slant the surface more vertically so the pen will be more horizontal and the ink should flow less.
When I'm finished, I spray glass cleaner on a paper napkin and wipe the nibs thoroughly until they are clean. The glass cleaner does a great job getting the ink off my fingers, too!
My local store, Art Supply Warehouse in Westminster, California, stocks ink by Daler-Rowney (acrylic medium), Winsor & Newton, Liquitex, Private Reserve, and Speedball. Higgins Eternal Black seems to have the darkest black around.
However, calligraphers have used more than inks, and this includes gouache and other paints that can be thinned down and held in the pen.