First up, it seems that you need to expand into other genres more than changing platforms as you mentioned that you're a bit shooter-heavy in your game library.
Second, you're not going to get away from achievement whoring... that exists to some degree on PC with Steam & uPlay, but PC players generally aren't as concerned about your achievement counts or your Steam Level (which can effectively be bought, especially with some of the event badges having no crafting limits). Even with Windows 10, your XBox Gamerscore will follow you when playing the PC versions those games.
With that said, you can pretty much play most non-console exclusives on PC (so no Mario, Zelda, Halo or Uncharted... to name a few) with some extra flexability on controls, since you can use Keyboard + Mouse OR a controller... or some combination of input devices that PC & the games support. While I don't know exactly what you prefer, here's a good cross-section of games to consider trying out.
On the "Free to Play" (or "Free to Start" being the better term)...
* Spiral Knights
* Puzzle Pirates
* Realm of the Mad God
* Pinball FX 3
* Path of Exile
For more paid titles (in no particular order)...
* Terraria / Starbound
* GTA V
* Slime Rancher
* Dragon Quest XI
* Final Fantasy series (III - XV)
* Myst series
* Torchlight / II
* Dark Souls series
* South Park: Stick of Truth / Fracture But Whole
* Diablo series
* "Pen & Paper" series (Knights 1, Knights 2 & Galaxy)
* Papers, Please
* Return of the Obra Dinn
* One Shot
* Zero Escape series (999, Virtue's Last Reward & Zero Time Dilemma)
* Trucking Simulator series (European, European 2, American)
* Cities Skylines
* Project Cars / 2
* Stardew Valley
This isn't an exhaustive list (as I'm going over about 1700+ titles in my own PC game library to pull out the big hits), but I hope this serves as a starting point for you.