During the main game:
Stone Prisoner (Sulcher's Pass/Honnleath): Immediately. Make it the next thing you do before you go anywhere else once you're deciding where to go next. Beyond how great it is as a DLC, the companion has a LOT of things to say pretty much elsewhere. No spoilers, but you definitely want to do this one in full before going to Orzammar to talk to the dwarves.
Warden's Keep (Levi Dryden, Camp): Pretty much any time. "Retake an old warden fort" makes a LOT of sense for the early events of the game OR shoring up your past closer towards the end. Literally whenever. I usually play this early.
Return to Ostagar (Bann Loren's Lands): I typically do this when I've recruited either two or three factions. Not at the end but definitely not the beginning. It's a nice point for reflection. I know you said spoiler free but read this one: Take Alistair ESPECIALLY and, if she lives, Wynne, with you. Trust me.
EPILOGUE: Everything from here down should really, really, really, really only be done after you're finished with the main game - and if you plan to import a save to Dragon Age 2, it's important you do them in these order. You can *skip* one/two/three (I almost always skip one) but if you DO them the order can potentially screw with DA2 imports.
Awakening: This is where you'll go when you're done with the main game. It's easily a full 1/3ish of extra game. You can either continue your Origins character or create a new Warden from Orlais (if you do this, you'll start at level 20). This also sets up some things for Dragon Age 2 and has one of my favorite/most intriguing characters in the series.
Golems of Amgarrak: Of the epilogues, this goes in the middle. It's also the one I almost always skip. It has some of the most difficult combat in the franchise especially at higher settings. (That's not a spoiler, it practically says it on the tin). Also, only 1-2 tiny little things have anything to do with the main story. For your first run it's worth a play, and you might well LOVE IT, but this is easily my least favorite add-on in the entire franchise. If you play it, do it in the middle.
Witch Hunt: This is the end of the story for Origins. Always play it last. It's relatively short, but it ties up a loose end while creating some new ones for later. That was suitably vague. Mandatory in some conditions/world states, damned interesting (and quick) in all others.
STANDALONES: These can be played literally whenever and the story connects to the core game but you will not use your player character and are designed to tell certain in-universe stories. Do each at least one time.
Leliana's Song: Assuming you recruited the redhead chantry sister in Lothering, this DLC will tell you a LOT about her life before she met you. Very interesting and intriguing story. Also, no spoilers, but you should definitely have played this at least one time before playing Inquisition (3rd game) later on if playing in order just for a little extra emotional weight.
Darkspawn Chronicles: Very much worth a play, but usually only once. It's an alternate universe/what-if of part of the game where your player character died at Ostagar and you control a darkspawn. (won't spoil the story otherwise). This won't be something you come back to if you replay the games but it's a blast to play once.
ALSO: If you're on PC, there's one additional VERY short official prologue DLC, A Tale of Orzammar, that is not bundled with the game that is very interesting to play through, especially if you're interested in the dwarves and even more if you pick the dwarf noble origin. Very super short. More info on the Dragon Age Wiki here (A fantastic resource in general BTW as you get deeper into the games, and yes, they typically try to hide spoilers by default)