Lightboost?
G-Sync/FreeSync?
IPS?

#1829
Please use the bbcode export from pcpartpicker, not a screenshot.

Also it's a trainwreck.

Let's start at the bottom:
I've written way too much about why no one should buy the VG248QE anymore already, google it or just believe me.
Do you want Lightboost or G-/FreeSync?
The PSU is ancient and overpriced.
I don't particularly like the case but that's for another day.
That specific 1060 is underwhelming.
The WD Black doesn't make any sense. It's not any faster than a Seagate Barracuda, but much more expensive. Also you have an SSD, why would you even try to buy an HDD for speed?

Now for the big issues:
You have a low profile cooler and a Mid ATX tower (the opposite of low profile).
You have a -K CPU (overclocking) and an H170 mobo (no overclocking).
What are you trying to accomplish?

Yeah, although for TF2 the 6600 might make sense. The 6500 is "only" 10% faster than a 3570. Yes, you can't get that with the 3570 but if you spend 350€ for the best performance you should really go all the way.
If you can find a 3570 it's obviously going to be far cheaper.

Yeah, upgrade the CPU first and see what happens.

I'm a bit late.
Why did you not take KiNG up on his offer? 40$ for a 260X is great.

For streaming (you mentioned that in #1) try to find an i7-2600 or i7-3770. 2600K, 2700K or 3770K are also fine, but not faster, since you can't overclock with your motherboard.

GPU depends on what settings you're going to use. Let's just play safe and get something about 3 times as fast the 250 (drops to 40 but you want 120). That would mean a 270 or 370 used or if you want a brand new GPU an RX 460.

Kind of ruins the whole "as cheap as possible" with ~50$ for an 250 (if it was new) and now 100$ for a 460 instead of going straight for the 460.

Well either get a used i5-3570 (should be fairly cheap) since I doubt your mainboard supports overclocking or get a whole new combo (CPU + RAM + mobo). I might be able to squeeze in overclocking with the 400€ budget but it's going to be tight. Obviously not a problem if you don't want to overclock anyway.

#1823?
Budget?

#1821
You should not be thermally limited. Mostly depends on the CPU (although for Skylake there isn't much spread) and you.

#1/#10
I like how Thaigrr hasn't been spelled correctly even once so far.

Depends on how over the top you want to go.
NH-D14 is good, if you want something even bigger you'd have to go for a different case.

Assuming you've still got a cooler:
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i7-6700K 4.0GHz Quad-Core Processor ($328.89 @ OutletPC)
Motherboard: ASRock Z170M Extreme4 Micro ATX LGA1151 Motherboard ($91.98 @ Newegg)
Memory: Kingston Savage 16GB (2 x 8GB) DDR4-3000 Memory ($79.85 @ Newegg Marketplace)
Case: Phanteks ECLIPSE P400 ATX Mid Tower Case ($49.99 @ Newegg)
Power Supply: EVGA SuperNOVA G2 550W 80+ Gold Certified Fully-Modular ATX Power Supply ($64.99 @ Newegg)
Total: $615.70
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-11-11 18:05 EST-0500

Depends on prices though.

CPU deals are rare, but everything else (RAM, mobo, PSU, case) should happen. Not sure if there'll be something useful for you, we'll just have to wait and see.

1. Soon™. 1 or 2 months, probably January.
What kind of leap would AMD be? You can't even tell the difference. Unless you need TSX but Intel hasn't got that to work yet and I doubt you're running databases on your PC.

2. I'm not saying the 6700K isn't the best option for performance right now but I expect massive buyers remorse.
It's not future proofing when better options are available for the same price 2 months later.

I mean your options are:
Overclocking your 2500K higher - 0$
2700K - 150$
6700K + mobo + RAM - >500$,
7700K + mobo + RAM - same price as 6700K

Single threaded the performance gain would be:
2500K OC - 20%
2700K - same as 2500K
6700K - 10-15% over 2500K/2700K
7700K - 10% over 6700K

Multithreaded:
2500K OC - 20%
2700K - 30% over 2500K
6700K - 20-30% over 2700K
7700K - 10% over 6700K

There's also Zen but single threaded performance and price aren't completely clear yet.
6/8C will definitely be far better multithreaded, but at best it should compete with Broadwell-E single threaded, not Skylake or Kaby Lake (still as good as a properly overclocked 2500K).

3. You can't fit more than 2 GPUs on a µATX mobo but since you can't do that with LGA1151 anyway there really is no downside. Cooler height limitations depend on the case as always.

#1809
Ok then. Still for future proofing you're going to have a bad time with the 6700K.
Average OC is 4.5GHz. The 7700K is supposed to come with a turbo of 4.5GHz.
Also Zen.
And the year after that there'll be Coffee Lake with 6 cores.

Micro ATX are cheaper and micro ATX cases are cheaper as well. There's just no downside.

#1810
Shadowplay records with minimal fps loss and automatically records the last x (whatever you set it to) minutes when enabled.
GVR/raptr/plays.tv records with minimal fps loss and automatically records the last x (whatever you set it to) minutes when enabled.
It does the same.

Maybe Intel driver bullshit.

4GHz isn't a very good overclock for a 2500K.

Base clock on the 6700K is 4GHz, turbo 4.2.

In that case you might as well wait for Kaby Lake.