Note that some abilities scale up with increased AD (like Trundle's Chomp), some scale up with increased AP (like Tristana's Rocket Jump), some scale up with both AD and AP (like Evelynn's Hate Spike), and some scale up with another stat (like Taric's Shatter scaling with increased armor, or Volibear's Frenzy scaling with increased health).
You can tell the scaling by looking at the color of the (+??) in the tooltip. Orange means AD, light blue means AP, and other colors will be explained in the description.
If you're experienced with SC2, you won't find any champions that require very high micro skill (you only ever control one additional unit at most, and that's only with about 5 champions out of 113). You could start with a champion with a high skill cap, if you like. Maybe Jayce, Zed, or Lee Sin. It looks like none of the free champions this week are mechanically complex, but they change every week.