I'd recommend playing in release order if you're someone who tends to enjoy delving into lore. (And man, is there a LOT of lore.) I did them in reverse order originally, and although I enjoyed DAI a lot, I didn't quite get why the stakes were so high for the protag. I felt way more connected to the storyline when I returned to Inquisition after having Origins and DA2 under my belt.

My other reason for recommending chronological order is that Origins is one of the best games I've ever played. I still fire up my Xbox 360 to give it a play now and again.

Origins struck a good balance between player autonomy and the required storyline. You can pick your character's race, gender, and class at the start of the game and get a unique back story that informs how you can approach later conflicts and circumstances. Then you find out the central conflict and are presented with the different factions you need to draw together. From there, it's up to you to decide who you'll support and how you'll make it happen. You can be a true asshole to all your companions, or a Lothario, or BFFs. And the combat system is pretty good overall, despite being dated and a touch clunky. The party mechanics are fun when you get used to them.

DA2 is a perfectly serviceable game, but not one I personally enjoy replaying. Humans are the least interesting race in Thedas to me, and I'm sure that contributes.

DAI is definitely an Open World Game and therefore plagued by all the struggles these games tend to have, but I still found it really fun. Jaws of Hakkon is a great DLC for the world building element. Trespasser is basically the real ending of the game, so hopefully you'll have access to that DLC as well!

I hope you have a great experience playing these games for the first time! DA is my favourite series ever, and I love seeing folks give it a go. :)