There's something to be said about to going into graphics settings, maxing everything out, and getting 240 FPS without a dropping frame. That's 1080p right now. Nothing wrong with it. You can be frugal and have a blast.
Problem is 1440p is kind of table stakes when it comes to monitors and components right now. You can pick up a 27" 1440p 144 HRz gaming-branded monitors for a couple hundred bucks, less if you shop around. It's close enough to 4K resolution without needing a high-end card to push 120+ FPS even at high settings. Best of both worlds.
So my concern about focusing only on 1080p would be the fact that it's going to get very old very quickly, especially in the next few years. 1440p is where you should aim. Low end display tech tends to get very old very fast.