You can't really talk about adding sugar to the beer in terms of general pros and cons. For some styles of beer, the effects of using sugar will be beneficial, but in most styles, it will be harmful. I have brewed styles with sugar (because it came with the kit) that do not typically use sugar in the recipe, and the beer didn't turn out very good. Look at some recipes for your style of beer on the forum to see if they use sugar. The risks of using sugar are very low, since there are no disadvantages to just boiling it to sterilize it (unless it's flavored sugar).
The recipes for which I used sugar, had me adding dextrose during the boil along with the malt extract. If you've already started fermenting, then I would treat it the same way I treated honey when I added that during fermentation, which is to add it just after high krausen. It's best to watch the krausen level to determine this (I made a point of using a carboy for that batch so I could see), but it usually occurs in the second or third day of fermentation, in my experience.
As for type of sugar, it depends on the style. The Belgians usually use some kind of special candy sugar, but I don't have any experience with that. Dextrose has the reputation of fermenting the most cleanly, which is why it's popular as a priming sugar.