Wait for Vega 56. It will be rather power hungry though, but not as bad as Vega 64.

Well looking at it's specs, i doubt it will be that much cheaper than the 64 that i could afford it. Would be nice if they proved me wrong though, i'd very much like modern gl and vulkan support with the card, but i'd doubt my 150-200 euro will be enough.

With this budget and the current market prices, this won't be easy.

The closest within that price bracket would've been RX 470/570 but only if you can actually find it at original price.

If you are adamant about going with AMD, you might get lucky with Sapphire Pulse RX 580 8GB on pre-order from Amazon. It's listed at £220 though the waiting times are very long.

A 3GB 1060 is reasonable mid-term solution if you want a card right now. It might be the only mid class GPU that doesn't have massive price offset at the moment.

Since you want the card to last for 4-5 years, try with RX 580 8GB on pre-order at the original MSPR. Most likely, you will wait a month for it.
One caveat of the RX series, is that you need to run a recent kernel for your distro. The newer the kernel, the better. If you are on this website, there is no way you could've missed all the updates of how the open source driver for those cards is progressing :)

Or save up for Vega 56 as @Shmerl suggested. It doesn't look like Vega is better for mining than Polaris, nor would it be affected of this August GDDR5 price hike as it's using HBM2.The current price shenanigans with Vega might be just the usual market reaction of new hardware. We will know for sure in a couple of months when the AIB Vega cards hit the markets.

Personally, I won't be able to upgrade my ageing GTX 660ti before the holiday season. I will grab whatever makes most sense at the time.

Thanks for the tips!

I looked through some sites to find some of the stuff i wanted used in order to save some money. However, it seems, that for every item i save the most if i order through german amazon site, so vega and the rx 580 seem out of reach. But i found the Sapphire Pulse Radeon RX 550 card, which is just $123 on amazon, it seems to fit the price tag. Could that card run the new Hitman game in 1080p?

Honestly, I don't know.

I wouldn't buy the RX 550 at this price, however. The RX 560 4GB can be found at the same price and it's a better card, period. Unless you have PCIe only power requirement, which I doubt.

You can check Phoronix and try to find benchmarks that would give you reasonable point for comparison. This one is from May:
http://www.phoronix.com/scan.php?page=article&item=radeon-rx-560&num=4
The difference between the 550 and 560 is very noticeable. Yet, both are significantly slower than the RX 580 or the GTX 1060 (even the 3GB version).

In your case, I would either grab a 4GB RX 560 at the lowest price I can find or take the GTX 1060 3GB for 20-30€ above your price range.
The GTX 1060 will run everything very well at 1080p. Maybe you will have to lower the texture resolution at some point. Running on Linux, means close source NVidia drivers which aren't bad.
But for the performance difference, I would pick the NVidia card instead of the low end AMD card. Nothing can change the fundamental hardware capabilities. If the budget is more important, then RX 560 4GB as close to €100.

I'm not familiar with the German retailers and what deals you may find. So checking on other forums or irc channels would be good.

I was about to order the rest of the stuff, but i didn't in the end. I really find the prices of the RAM memory and the graphics cards too high to worth buying. My only hope now is the december discounts, although i doubt that will significantly change the price of stuff.
Anyway, thanks to Shmerl and Pakost for the helpful answers!

I know the feeling.

Hopefully the prices of the RAM modules and mid-class GPUs will normalize for the Holidays.The next couple of months will get even worse before we see some normal prices though.

On the RAM side, it seems like the holiday season is perfect. Almost half of DDR4 is allocated for smartphones (iPhone 8 and Note 8 are prime suspects with their high volume sales) which will drive prices even higher in Q3. The smartphone upgrade cycle is at its lowest around Christmas and New Years with almost no new releases. Perhaps Google's Pixel phones will finally be available in a bit higher quantity around that time (if history repeats itself :D ) but it won't make a huge dent.
For a budget build, 8GB (2x4) DDR4 is enough to be honest.

For GPU prices, who knows. Maybe we will see the same RX 470/570 prices as the last holiday season with sub 200$ prices (if there is no new crypto currency that will emerge and be hugely profitable). Vega 56 looks like a very compelling option regardless.

Lets hope for awesome holiday builds and nice Christmas presents!