In answering this question, I'll restrict attention to the most often chosen first colors, blue and black (and blue-black). I'll consider three criteria:
Reliability (R): Some inks will work well in most any pen you put them in. Others won't. Since I want you to have the best possible first fountain pen experience, this is a key criteria. The rating scale is Excellent, Good, Fair, Poor.
Flow (F): Some inks are free flowing and will give a wetter line for relatively dry pens. Others are less free flowing. Some pens that already have generous ink output do better with less free-flowing inks. The rating scale is: Free, Medium, Not Free.
Saturation (S): The more saturated the ink, the darker and less watery the color. The rating scale is: Dark, Medium, Light.
Waterman Florida Blue. R: Excellent; F: Free; S: Medium;
If you only own one bottle of ink, this should be the one. Works well in pretty much every pen, looks good, lays down a wet line. The only drawback is that Waterman ink has a funny smell that some people dislike.
Waterman Blue-Black. R: Excellent; F: Free; S: Medium
Another nice Waterman color. Takes you back to bygone days of sleeveguards and eyeshades. A good choice.
Waterman Black: R: Excellent; F: Free; S: Light
This is kind of a washed out black. It's reliable enough, but not a nice color.
Aurora Blue. R: Good; F: Medium; S: Dark
This is a darker and deeper blue than Florida blue. It's very attractive. Will not perform all that well in very dry pens.
Pelikan Brilliant Black. R: Good; F: Medium; S: Dark
This is a nice dark black in relatively wet pens. In drier pens, it can be more grayish, which is not nearly as nice. Overall though it's a better black than the Waterman.
Sheaffer Skrip Blue. R: Excellent; F: Free; S: Light
A perfectly reliable ink, but the color is a bit washed out.
Levenger Cobalt Blue. R: Poor; F: Not free; S: Dark
This ink is very seductive. When it's working well in a pen, it's a gorgeous deep shade of blue. There have, however, been many reports of pens having problems with this ink. Stay away.
Montblanc ANY COLOR. R: Poor; F: Not free; S: Light
Despite its pedigree, this ink has nothing going for it. Avoid.
There are a number of other places on the Internet that review many more inks. Here are some highlights:
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