Been a fan since the start, so here's my two cents:

Dragon Age Origins is amazing. Buy each of the expansions. Save files transfer from expansion to expansion, and there are also a few DLCs for the base game. Usually everything is sold in one package - either the Ultimate Edition on Steam (which can also be modded), or GoG. GamePass only has the basegame.

Once you've completed the final DAO expansion (Witch Hunt), DA2 is worth playing at least once for its story. It has two expansions (Mark of the Assassin and Legacy) both of which are improvements on the base game. Don't bother with any other DLC unless you get it all in a package deal. Save file transfers directly into DA2 from DAO.

Once you've completed DA2, DAI is also worth playing (I personally liked it more than 2, but YMMV). Mainline it if you start getting bored, as the main quest is worth the playthrough. It had three expansions, the first two played during the main campaign (both endgame) and one postgame expansion. All are worth playing, but The Descent and Trespasser are the most important for the overall world. DAI saves are a bit weird, as they don't come from DA2. Instead, you fill in your choices in the Dragon Age Keep (should be first result on Google) and export them to DAI. I suggest jotting down major choices as you go.

Outside of the three games, there's also a series of novels and a Netflix series, as well as a series of comics. The first five and following three comics are available in collections, generally pretty cheaply. Novels are printed to order. If you enjoy the stories in the games, I strongly recommend Asunder by David Gaider and The Masked Empire by Patrick Weekes. Tevinter Nights was great, but it may lose relevance when the new game comes out in the coming couple of years, as it was written as a kind of preview for what's coming up. The Netflix series was good, but likely of little relevance to the greater narrative.

Honestly, all three games are worth playing in order. There's nothing atrocious about any of them (DAI won game of the year in 2014), although none have aged super well. In the case of DA2, it may be worth mainlining if the environments bother you (game was made in 18 months, so most maps were recycled several times). If you do mod DAO, just do texture mods for now; there's some great stuff out there, but only really worthwhile for later playthroughs.

If you find yourself really loving DAO, Baldur's Gate 3 is a spiritual successor to it and a direct sequel to the games that were DAO's original inspiration. Do check that out when it comes out at the end of the week if DAO is your jam.

Feel free to DM me if you have any other questions!