I'd suggest trying DA2, because even if you dislike the game itself, the characters make it still very enjoyable.
But a basic summary of the plot;
Hawke and their family are refugees from Lothering in Ferelden, who journey to their mother's home of Kirkwall in the Free Marches to escape the Blight. Either Hawke's sibling Bethany or Carver will die during the prologue, depending on their class: Bethany if Mage, Carver if Rogue or Warrior.
Fearing either themselves or their sister being discovered by the Templars who control Kirkwall, Hawke is convinced to join Varric on an expedition to a Lost Thaig in an uncharted and forgotten region of the Deep Roads, hoping to make a fortune for themselves. However, this requires first amassing enough coin to convince Varric's brother Bartrand to let them become a partner, setting up their main objective for the first Act. Along the way they meet various companions and meet with the Arishok, the leader of the Qunari, who is in Kirkwall for mysterious reasons.
Hawke goes on the expedition, where they are betrayed by Bartrand after discovering a Lyrium Idol made of a hitherto-unknown form of Red Lyrium, forcing them to find the long way out of the Thaig. The fate of their sibling is decided depending on their actions thus-far. If Bethany or Carver was left behind, she decides to go willingly to the Circle, while Carver becomes a Templar. If brought along to the Deep Roads, the sibling will contract the Taint and die, unless Anders is also present, who is able to direct them to some nearby Grey Wardens, who induct them into the order to save their lives.
Act 2 picks up three years later, with Hawke now a rich noble in the city. The Qunari have still not left and are growing increasingly restless, leading to the Viscount asking Hawke to become his go-between to the Arishok, as they are the only person he's willing to deal with. In between this, a Chantry Sister that Hawke had previously met is stirring up violence against the Qunari "heathens", further making Hawke's job difficult and eventually leading to the murder of the Viscount's son, who is a Qunari sympathiser.
Finally, it's reveal that Isabela had stolen the Tome of Koslun, the Qunari's sacred text, but had lost it and has spent most of the past two acts trying to track it down to save her own skin. After recovering it, she skips town and this coupled with his growing frustration with the chaos he's been subjected to in Kirkwall, leads the Arishok to mount an invasion of the city. If Isabela's friend or rivalry is maxed out, she can return and attempt to placate the Arishok, but he demands she be handed over as well, which Hawke can do (if you're being cruel). Either way, Hawke eventually defeats the Arishok and is declared Champion of Kirkwall.
Act 3 picks up another three years later, with Hawke attempting to deal with the deteriorating crisis between the Mages and the Templars. Meredith has also become far more brutal in her crackdowns against suspected Blood Mages, not helped by her sword being revealed to have been forged from the Lyrium Idol found in the Deep Roads all those years previously, which affects her sanity. Anders has also become increasingly unstable because of the Spirit of Justice residing with in him, eventually leading him to blow up the Chantry to incite a rebellion.
The ending is Hawke deciding whether to support the Mages or the Templars to restore order in the city, facing off against Meredith in both cases. In the former, they attempt to prevent the Templars from enacting the Rite of Annulment and afterwards, eventually flee the city. In the latter, they become the new Viscount, but eventually are forced to leave for unclear reasons.
Three years later, the world is on the brink of war and Varric has been captured by the Seekers to find out more about Hawke, who wish to know the truth behind the myth. After finishing relating the tale to Cassandra (i.e. the game we've just played), she decides to let him go and is revealed to be working with Leliana, who's now working as an Agent of the Divine and also trying to stop the war.
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Okay, that wasn't that basic, but it's pretty much all the main plot points.
