Does the water need to boil or just be hot? Do I need to put salt and vinegar in the water or just salt? And if it needs vinegar, what kind? How long do I leave it in the water to get the white solid but not the yolk? I do not like raw egg white, so this is very important for me. But the tricky part is to have the yolk nice and runny though...
By far the most important factor in a nice poached egg is the freshness of the egg.
Fresh eggs shouldn't need vinegar to help them set, but It can help with an older egg, whose white has started to go a bit runnier. Vinegar does leave a flavor, but if you're poaching your eggs ahead of time and putting them in iced water to stop them cooking, that does seem to wash it out.
Salting the water will toughen an egg, better to season it after it comes out.
A large egg, starting at room temperature, in barely simmering water (trembling) will take 3 1/2 minutes to just solidify the white, and leave the yolk very fluid. If you want your yolk more viscous, another half minute.
In my experience, while vinegar will hold the whites together a bit, it can toughen the egg, and adds what I consider to be an unpleasant taste. If your concerned about keeping the whites from spreading and streaking, use a fine mesh tea-strainer to get rid of the excess moisture from the eggs. This will also help the egg white solidify faster without affecting the cooking of the yolk.
As for the water, it should be barely simmering.