wireless display

I am finally getting a monitor for my SP3 and trying to figure out if I can get away with connecting via a WDA. I will be using Photoshop/Lightroom and will have a nice monitor so I want to maximize the resolution. Is there any difference in a wired and a wireless connection? Thanks!

It isn't working for some reason. I go to FireTV -> Mirroring, FireTV says "while this screen is open guest devices can wirelessly mirror their display". On Surface, I've tried both Connect and Display -> Wirelessly Connect, in both cases the "searching for wireless display" window comes up but...