I personally use a PS4 controller myself, and have used a 360 controller in the past, but I never used them wirelessly. However, that won't matter. In terms of what controller I prefer, I prefer my PS4 controller greatly. The PS4 controller has a vastly superior d-pad over the 360 controller, and if you are going to play 2D games then this is a must I think. Otherwise, they're fairly similar, I just like my PS4 better (I just prefer Sony I guess).
As for that Logitech controller, I've never used a controller from them before, but my Keyboard, Mouse and Headset are from Logitech, so they make good stuff.
Honestly, all controllers will work, it will just be down to what you prefer to use. Download InputMapper and test out your PS4 controller. The PC will just think it is a 360 controller.