For DAI, I HIGHLY RECOMMEND that you play DA2 and its DLC Legacy. It IS relevant to DAI, along with one of the DA2 followers who is also in DAI.
Because the import system tended to be a bit buggy, they changed the method of using save files for imports. Dragon Age: Inquisition uses the Dragon Age Keep, and it is what all future games will use as well.
Dragon Age Keep site.
DA Keep on the official forums.
I'm not sure what version of DAO you have, but there is also the Awakening expansion and the DLC. If you play that as well, then your save import order goes like this:
Dragon Age: Origins
Dragon Age: Origins - Awakening (expansion)
Golems of Amgarrak (DLC)
Witch Hunt (DLC)
Dragon Age 2 (play Legacy either during the main DA2 play, or after).
So you import from DAO into DAA, from DAA into Golems of Amgarrak, from GoA into Witch Hunt, and from Witch Hunt into Dragon Age 2.
But... it should be noted that DA2 does not use any information from the two DLC -- GoA or WH -- so you don't have to use that import path and can just go from DAA into DA2.
After playing DA2, you go to the Keep and input all of your choices BY HAND. I know it's an annoying process, but there were technical limitations. You can upload your Warden and your Hawke into the Keep, but the only information that it takes is your origin, race, gender, class, name, and character portrait, nothing else is used for those two games.
The main benefit of using the Keep is that you don't have to use the exact same choices you made in all of the games. If you want a different result for a Big Decision, you just change that in the Keep and that is what DAI will import.
Dragon Age: Inquisition updates the Keep as you play because that game is fully integrated.