Most darts nowdays are anywhere from 12 - 18 grams. The lighter dart will fly easier to the board with less effort, but the path of the dart can be changed by the slighest disturbance or change in the throw. The heavier the dart the more effort needed to throw it, but a heavier dart will be more accurate. Only drawback is you need to keep a consistant throw or the heavier dart will tend to drop. Try throwing lighter and heavier darts to decide which weight feels better to you.
Darts come in a few differnt diameters from a bigger diameter to a skinny diameter.
The diameter will come into play as you learn to throw a tighter grouping of darts, the bigger the diameter the more chance of hitting another dart and deflecting into a differnt number then the one you wanted. Darts come with a few options as to grip. You can get a smooth barrel, a barrel with some grooving on to increase your grip, some barrels have dips in the barrels for your fingers to grip, and some dart sets come with rubber sleeves on the barrel for grip. Try throwing differnt kinds of barrels to see which grip feels right to you. Darts lengths are determined by many factors.