how is his video card going to affect the monitor choice
Two reasons. 4K support, and the program they are using for "kereoke" is completely unknown to me, im not taking any chances with it (even though it most likely doesn't use a drop of GPU power, im not supposed to assume.)
Mainly, if they want a 4K monitor, they need a GPU that supports it.
So the question here is, Alyx, do you want a standard 1080p monitor or something more like a 4K monitor? But considering your "pricy as hell" statement earlier, I'd like to think 4K isnt possible at the moment, as Newegg's cheapest 4K PC monitor is $1,199.99. But those will go down over time as more 4K monitors are released.
So, with that in mind, you'd probably want a 1080p monitor something like an Acer G6 G276HLGbd, a 27" 1080p monitor for $199.99. 1080p monitors are between $100-200 usually.