Looking for games with stories!

[Alpha]

Star Wars Knights of the Old Republic 1 & 2.
They, especially 1, beat the shit out of 90% of the shooters mentioned already in terms of storyline (and plenty of other categories IMO).

Good news is they're 6-8 years old too- not dated, but your computer should handle them.

Final Fantasy 7, 8 and 10 too.

KOTOR 1&2 were great games, definitely getting the 3rd!