Re: DLCs worth playing of all 3 games (DLC names and order)
My recommendations:
Dragon Age Origins
The Stone Prisoner - An additional character. This doesn't have any effect on the sequels, but Shale is a great character throughout the game.
Awakening - I think this is some of the best content in the entire series. Awakening doesn't affect DAI, but it contains two characters who are involved in DA2, so it's great to have some context.
Dragon Age II
Legacy - This DLC is is important if you want context for Dragon Age Inquisition. I think this DLC is best played right at the start of the third act.
Dragon Age Inquisition
Trespasser - A post-game DLC. Great story that brings closure, and it also affects skill trees throughout the game.
Tip: Always check to see if there's a sale going on. You can often find Dragon Age Origins - Ultimate Edition really cheap, which is handy as it contains all the DLC. At the moment, the Ultimate Edition is 50% off where I am (France) in Origin so it may be a better deal that buying the DLC separately. If you miss the sale, you could wait a while and get it during the Steam sale.