Is building your own machine completely out of the question?
Starting from scratch will enable you to get exactly the stuff you want/need, without either having to compromise somewhere or pay an outrageous sum for a "boutique" system.
Some of the pre-builts from your site don't look so bad to me, though. E.g.:
http://www.ldlc.com/fiche/PB00132339.html (would need a SSD and Windows in addition)
And not that much more expensive given that it has decent components.
If you do not care for high(est) graphics settings, and use 1080p display or smaller, a reasonable option would be a business line PC from the likes of Lenovo, Dell or Fujitsu coupled with an energy efficient entry-class gaming video-card like the GTX 750 Ti.
Something like that should be found for about 800 for a i5 system with a 256GB SSD and a 750Ti.
Contrary to what was recommended, for strategy games a i7 is pretty much pointless.
Civ 4 and 5 AIs run on a single core, and as far as I know it's the same for the TW games. It's improbable that Civ 6 will be different.
For powering the graphics a i5 will be plenty enough, too.
In any case, you will want a SSD as pretty much the first priority. It's that much of a difference, not so much for gaming (loading times will get better), but for general usability.
It looks increasingly likely that new games will see a jump to 4GB VRAM as a requirement for "really pretty" graphics settings fairly soon-ish (a year or two), and maybe even for minimal requirements not that much later, so be careful if considering getting a fairly powerful/expensive card with "only" 3 or even 2GB VRAM.
It might become obsolete faster than comparable cards in the past.
Getting a less powerful card with the perspective to replace it in about two years (or when Civ 6 comes around and needs more juice) might also be an option, the GTX 750 Ti for example should be fine at present for any game on your list.
And yes the GTX 970 is indeed THAT good in nearly every aspect, but there are models that are not very quiet (or at least get loud when running at full load).
You should be able to use any screen with any modern graphics card, but VGA-only ones should indeed be avoided. But those are mismatched to a 1000+ machine anyway.
Some of the less expensive 4k displays run only with 30Hz on a PC, those are to be avoided, too.
And with a 4k display, you should consider a card in the GTX970 class.