Need Advice, what should be priority GPU or Monitor First?

You could do either really. But I would say the monitor first because going past 60fps on a 60Hz monitor doesn't really give you any upgrade. With G-Sync and 144Hz and 1440p is very nice it gives extra detail and you can still run fairly high settings.

I would advise you to upgrade your gpu first. If you upgrade the monitor first, games that you used to be able to play may not run or run well at the very least. If you upgrade the gpu first, your monitor will not use all of the power, but a bottleneck like that is still better than not being able to play games with.

Yeah, 1440p is more demanding due to the GPU needing to render more pixels. In general, you'll get around 30% lower frame rates at the same settings at 1440p compared to 1080p. And a GTX 970 isn't exactly a great card for running the latest games at 1440p, so you probably won't benefit from the high refresh rate in most newer titles.

As another possibility, maybe it would be worth making a compromise, and getting a graphics card upgrade, plus something like a 24" 144Hz 1080p screen without G-sync, which can be found at much lower prices, with some as little as US $200. I'm not sure if that would fit into your budget though.

The RTX 2070 will likely be launching for a higher price than the GTX 1080 is currently selling for, and I suspect it will only offer roughly similar performance to the GTX 1080 in most existing games, so the 1080 might not drop drastically in price right away.

One thing that's still unknown is how well the RTX card's new features like raytracing and DLSS will perform though, in the games that support those features. So far, those features simply aren't available yet, but it's likely that some games will add support for them over the coming months. How good they end up being could affect how much of an impact those cards have on the GTX 1080's price, so it's difficult to say for absolute certain right now. If the features turn out to be great, it's possible that you might even want to consider going with a 2070 instead, provided it isn't priced too unreasonably compared to the GTX 1080.

Or perhaps AMD will launch new cards sometime during the coming months that are more competitive in this performance range. Not a lot is known about AMD's next cards, or when exactly they will be coming though. In regard to that, AMD's cards utilize FreeSync rather than Nvidia's proprietary G-Sync to enable adaptive sync, and since it's something of a standard that doesn't require an additional chipset in the monitor, FreeSync monitors tend to cost less. Unfortunately, AMD's cards can't support G-Sync, and Nvidia isn't willing to support FreeSync, so if you want to utilize adaptive sync, you'll currently need to get a monitor that supports the appropriate technology for the card you end up going with.

Also, I'm not sure exactly how pricing compares where you are, but in the US, prices of GTX 1080s have already been coming down in recent months, at least at online stores. There's also the 1070 Ti worth considering, which is more of a pared down 1080, and is generally closer in performance to that card than to the 1070.

It's kind of difficult to say for certain right now what the stability of pricing for graphics cards will be like over the coming months. I suspect that monitor pricing might remain a bit more stable, though. However, I'm not sure that your 970 will have the performance to run 1440p particularly well in many games.

For the most part your i7-6700 (is that correct? you said 6600 but that would be an i5), your i7 would be good enough as well as 16GB RAM. You could get more performance out of the i7-7700K, but it isn't necessary and I would recommend waiting until you decide to go with a full system upgrade to a platform with higher core count CPUs. Did you ever mention what power supply you have?