To better understand what to use, you have to understand what the yeast actually likes to eat. Yeast can only consume simple (monosaccharides) sugars. Of this, glucose/dextrose is preferred but it will also consume fructose and galactose. In order for it to consume more complex sugars (disaccharides and polysaccharides), such as sucrose (table sugar) or lactose (milk sugar) or starches (DME), it needs to create enzymes to break it down meaning it does more work for less gain. By this logic the best thing to use for priming would be glucose/dextrose as it produces the most CO2/gram with the least byproducts (enzymes can also break down your desirable beer elements altering the flavor and reducing shelf-life) and in the shortest time.
But not so fast. As others have mentioned your sugar itself might contain other ingredients. The most common for dextrose and confectioner's sugar is corn starch. In dextrose the amount is quite small (naturally occurring considering its source, though if you look you can find 100% pure) but in confectioner's sugar the amount is much more noticeable to the point where it can influence flavors (if you hate frosting this is probably why, try a french butter-cream instead). In sucrose and DME there are typically no additives which make for a much better option. The only issue with DME is that it can give you a bit more of a malty taste due to what it leaves behind after the yeast is done with it.
The last thing to consider is that the amount you need. In most low carbonation beers you're not adding much so you can probably get away with just about anything with sugar in a pinch (apple juice box? why not!). Even in high carbonation beers you probably aren't going to see enough enzyme by-products from sucrose or starchy taste from the corn starch in your dextrose to really notice.
In conclusion, while the science behind all of this is somewhat fascinating all you're after is a good bubbly beer that doesn't taste like licking a cake from the grocery store. You really can't mess things up by using either dextrose, sucrose, or DME. Since sucrose is typically the cheapest and most readily available a lot of brewers use it. A tip I can give is to throw it in the food processor or coffee grinder for a bit to make it easier to dissolve completely.