Can pretty much to agree to everything which is said here.
If you want a new monitor in your budget as well, you are somewhat restricted though.
I might actually do the opposite of what zloth mentioned though.
First I think 1440p (16:9) is the more standard format (instead of 1600p = 16:10) if you want to go high resolution but this might actually be a bit more resource costly (and more pricey) than what you want to couple your PC with.
Generally I'd proabbly say
1080p -> GTX 1060, from personal experience I can say that the gtx 1070 is already overkill
1440p/1600p -> 1060 might work okish, 1070 or 1070 ti are better.
Also IPS Panels are superior to TN panels (and more expensive) but imho it's worth it.
144hz are a plus over 60hz but more expensive.
And Gsync is an extremely costly extra feature, which imho is unnecessary on 144hz anyways.
I am personally using a LG 27MP68VQ and I would have recommended it as a very cheap option (~250€) but it seems like it's nowhere to be found in the US.
Edit: Found it on NCIX, costs 330 CAD there (260 USD).
So while you could pay like 700€ for a really good monitor which lasts for 5-10 years. It might be better to just buy a good albeit cheaper one for 250€ and replace it in 3 years or so, when 144Hz, higher resolutions and even gsync become more affordable.
The configuration you mentioned (i5 8400, GTX 1060, 16G memory, and 256G SSD/1TB SATA. ) is actually quite good. Personally I'd want to get a 500Gb SSD though, as otherwise you will start to constantly swap games on the drive and think about where you can get some free space from, which can be more annoying then a few fps less.
If possible I'd buy a CPU of the latest generation (leading with an 8) from the i5 segment.
The memory used on this type of chipset should be 2666MHz, make sure you don't buy the old "standard" of 2333Mhz. You can buy RAM which is faster, if it is cheaper, but it will fall back to 2666Mhz then, making extra money wasted put into faster RAM if you don't run an board made for overclocking (which would be board starting with a z and a CPU ending with a K).