What kind of games do you play? What are you using now? What do you want to improve about the gaming experience?
And about your original question: you better make sure you have a very powerful videocard if you want to use a 1440p monitor. Even with G-Sync. 4K Monitors might be nice for different types of usage. But if you are a gamer, then running your games on 4K is madness. The higher resolution does not weigh against the loss of framerates and options/eyecandy.
I'll be choosing a monitor sometime fairly soon after a 34", 3440 x 1440, 21:9, G-Sync arrives like the Predator X34 (and hopefully others). I like the Dell 34" but it's only a 60hz monitor. I know there are plenty of games that don't support ultra widescreen because of the 'competitive advantage,' but I don't see why that matters beyond multi-player.
I hear the slightly curved 34 inchers provide the most immersive gaming experience (for the games that support it), and are great for productivity on the desktop; there are times I wish I could have three spreadsheets up, or while browsing have a WMC window on the side with news to catch up on.
Better make sure G-Sync works properly with Diablo 3. Last year it was reported that G-Sync did not work at all with Diablo 3. And there are still reports of people having problems with the combination.
I don't know the details, and I don't know if this is still true. But you better check it yourself, before being disappointed. I guess a technical sub-forum at Blizzard would be the best place to ask.
And about your original question: you better make sure you have a very powerful videocard if you want to use a 1440p monitor. Even with G-Sync. 4K Monitors might be nice for different types of usage. But if you are a gamer, then running your games on 4K is madness. The higher resolution does not weigh against the loss of framerates and options/eyecandy.