Dragon Age Origins: ultimate Edition and the DLC...

The fun gifts are easy, you can bul all from Bodahn, in the camp. The Stone Prisoner, The Warden's Keep, and the Return to Ostagar you can start whenever you want (I think worth it as soon as possible). Stone Prisoner maybe the first, because you can receive a new companion, after the Return to Ostagar (if you forget to recruit Dog at the beginning, you can here, if I remember correctly), and the Warden's Keep.

Darkspawn Chronicle: whenever you want, but probably better after the game.
Leliana's Song: is not related to the game directly. This is Leliana's story, you can after the game.
Witch Hunt: after the base game.
Awakening: after the base game.

There is a document on the discthat explains which order to play them in moer or less. I tend to just follow that when playing DAO. But quite simply Stone prisoner, Return to Ostagar and the Warden's Keep DLC's all take place during the main story. So just doing these whenever you like durin the main story is good enough.

Awakening, Golem's of Amgarrak and Witch hunt all continue the Warden's adventures.

Awakening is the first one you should play as it picks up after the Blight where it's basically your job as the new Warden Commander of Ferelden's forces to rebuild the wardens and investigate why some of the darkspawn aren't retreating back to the deep roads as they should be now that the Archdemon is dead.
It's kind of similar to the main story in that it takes you all over an area of a map pretty much all over Amaranthine Arl Howe's former territory which has been gifteds to the wardens to use as a base of operations as thanks for what they did.

The dwarven one Golem's of Amgarrak is next. In this mini story your helping the dwarves investigate one of their former thaigs lost to the darkspawn in one of the earlier blights. The combat can be tough in this one so you might want to be careful but if you can survive the Orzamma rsection i nthe main story you shouldn't have too much of a problem but it is of similar difficulty.

Witch hunt is the last of the DLC's about the warden. In this one your looking for Morrigan who's kind of done a dissappearing act. In this DLC your just revisiting a lot of areas you visit during the main game following clues to try to track her down.

Darkspawn Chronicles an Leliana's song aren't linked to the warden in anyway as they don't even appear in them so you can skip these if you just want to focus on the wardens story.

Darkspawn Chronicles is basically the Battle of Denerim all over again although this time your playing it from the darkspawn's perspective instead of the wardens. You basically just have to kill everything that gets in your way including Alistair asnd companions as you have to fight them at times in this mission too.

Leliana's song is basically a story about Leliana and why she is how she is when you meet her in Origins. In this DLC you play as Leliana and you get to learn more about her background and how she came to be doing what she did when joining you in Origins. It's not the most exciting DLC but it's quite good. fun. I quite enjoy it but thast's I think that's because Leliana is one of my favourite DA characters but from a game and story perspective it's not the best DLC.

As I've said al the extra DLC is bes tplayed after the main game only the Ostagar, Stone Prisoner and Warden's keep are played during it.