What you are using the sugar for makes a difference. There are sugars that give the yeast something to make alcohol with, and there are sugars that also add flavors because of how they were processed. And there are sugars that some yeast won't ferment.
So what are you wanting you use sugar for?
If for priming your bottles, most any will do that is easily fermentable.
Invert sugar is good for adding flavor to your beer. Color too if you are using the darker inverts. But mainly when added in larger quantity than the small amount you'd use for carbonation. So you see it used during the main boil. Usually near or at the end.
If you use a different sugar for a beer than is called for in the recipe, then you aren't really making the same beer.