I like games with a good story.
So I usually play on normal first. Unless the only way to get the real ending or some achievement requires the harder difficulty. I did this with the Infamous games, Ducktales remastered, Kingdom Hearts and Bravely Default.
Other games I take to the next level buy getting their DLC. But I have to really not want the game to end and the DLC has to truly enhance/extend the experience.
Alan Wake, for example, had some great DLC.