Raw sugar is ok...the standard though for homebrewers is corn sugar....followed by dry malt extract.
Now saying that different sugars will have different effects. If there's any "flavor" in the sugar, say using brown sugar, after the sugar ferments any unfermentables that contribute to the flavor of that sugar will be left behind.
A couple of craft breweries prime their bottle conditioned pumpkin ales with brown sugar, and you definitely get the mollases flavor in the beer, it is excellent.
Also if you use different sugars, you may need to use different amounts of it to acheive the correct volume of CO2...google priming amounts for different sugars...there's a couple good charts floating around the web.