Mass Effect 1 is pretty simple in that regard. Save the Colonists on Feros (this one's minor but technically does affect ME3), Save the Rachni Queen on Noveria, do the Wrex Armor mission before Virmire, convince Wrex to stand down (easy if you get his family armor), Make sure to do the tasks on Virmire so Kirrahe survives, and Save the Council. Oh, and in the Bring Down the Sky DLC, save the hostages.

Some of the other stuff doesn't really matter but it'll affect dialogue (like giving Tali the Geth data). I'd still recommend doing as many side quests as you're willing because a surprisingly large amount get mentioned throughout the games - my favorite callback having to do with the Rogue VI on Luna.