I play this game using my xbox 360 controller in Steam Big Picture Mode :) just need to map your controller to the right buttons in steam big picture mode ;) it works perfectly with a controller. In steam big picture mode I had to turn down mouse sensitivity a little bit as it was way to responsive. the way I have it set up is :

left stick = W,A,S,D.
Right stick = Mouse Movement / T when clicking (execute for killers)

Left Button = Left Mouse Button (Click / Interact)
Left Trigger = Left Control (Crouch)

Right Button = Right Mouse Button (Dodge)
Right Trigger = Left Shift (Running)

D-pad Up = F1 (Point Emote)
D-pad Left = F2 (Follow Me Emote)
D-pad Right = F3 (Clap Emote)
D-pad Down = F (Open Shop)

Y = Q (Switch Through Selected Card)
X = R (Open/Close Doors and Windows)
B = E (Use Item)
A = Space (Actions Like Skillchecks and Vaulting Windows)

Start button = Esc

Try it yourself with these settings and it should work fine :) the only thing you need to get used to is interacating with the shop interface ;) but once you get the hang of it it's easy.

Enjoy everyone :D

(Side note, once it has been set up in big picture mode you can use steam like normal and it will still work)