Hmm, easiest way seems to be to go down my steam list:
Age of Wonders/Age of wonders 2 (If you like HoMaM3 then you'll probably like this series, it's a similar thing)
BloodBowl (turn based, american football parody (but nothing like American football) with fantasy races, 8 turns a half and bloodthirstiness is encouraged)
Civilisation V + Gods and kings expansion + soon to be out "brave new world" expansion (hours and hours of gameplay right here if you like the game)
Command and conquer (various in the series). Should be okay with just a mouse, cant recall anything that *needs* hotkeys, I certainly didn't use any [edit: Not Red Alert 3, not Command and conquer 4, skip both of those. Bad reputation and some of the things are fiddly]
Dawn of War 1, Winter Assault expansion, Dark crusade standalone expansion, dont get the soulstorm expansion as it's crud. Dawn of war 2 requires a bit more micromanagement even for the campaign because it's unit based so skip that and it's expansion too. (Dawn of War series is a Warhammer 40k RTS)
Don't starve ("The game's goal is surviving for the longest time, while avoiding starvation, insanity, and hostile enemies. The player can collect and craft a variety of tools and items as well as build various structures to aid in surviving.")
Dungeons of Dredmor (Roguelike, dungeoncrawler with RPG elements. It's tile movement based, one square/attack per turn, whatever you call that (isometric?). Abilities are activated by clicking and because it's turn based there's no timer.
Frozen Synapse (Hardcore tactical game. "players plan their moves at their leisure and turns are resolved simultaneously. Players attempt to win by giving orders to a small squad of armed combatants, most commonly with the goal of eliminating all enemy units." You plan by giving orders then simulating your turn and it will work out what will happen if you do what you just told it. If you like the outcome then you lock it in and when the enemy has locked in their turn it shows what actually happened [e.g.in you simulation the enemy went one way but in the enemy's orders they told the unit to go the other way])
Faster than Light (roguelike, spaceship game, you've probably heard of this one already?)
X-Com Enemy unknown (turn based)
Hope that helped give you some ideas and I haven't just listed ones you've already thought of