Upgrade Help: Advice and compatible budget graphics card needed

[Guts]

Hello,
since Andromeda just came out and it's my first game to look like crap if I want to run it smoothly, I'm finally looking for an upgrade.
My PC is roughly 5 years old and I only use it for gaming.

Information:
Budget: ~300€ (flexible depending on the result - I would buy a 900€ graphics card if it works well with everything else I have)
Games/Settings Desired: ME:Andromeda Medium
Country: Germany
Resolution: 1920 x 1080
Processor: i5-3570K @ 3.40GHz
GPU: Sapphire Radeon HD 7850
Motherboard: MSI Z77A-G43
Memory: 16GB
PSU: 650W

After reading up a bit on current tech, my conclusions are:
CPU is still fine.
Motherboard is old but I see no reason for a new one apart from compatibility with newer GPUs(?)

GPU isn't fine. After "benchmark-fighting" it against something like a RX 480 -which is often suggested- there is quite a margin.
I'm content with games running smoothly on medium settings most of the time.

I am afraid of picking a GPU which doesn't work properly (=underperforms) or doesn't work at all with my board. I don't know how to check that.
And I don't want a graphics card which will be bottlenecked by another part like my CPU.
I looked at the MoBo specs: https://www.msi.com/Motherboard/Z77A...-specification
( PCI-E Gen: Gen3 (16) Gen2(4) )
So I guess I have a PCI Express x16 3.0 and can plug any graphics card in but I can't say for sure.

I considered buying a completely new PC this year, but after checking my parts, I only see the graphics card as outdated.
I look hardware up every few years when I either want to buy a completely new rig or need an upgrade so I am far from knowledgable about it.

I would be happy to know if anything I wrote is incorrect and what would be a good upgrade to keep my PC up to date if possible and by changing as little as possible.

TLDR:
Please suggest a budget upgrade for my rig and if it really is my graphics card that is holding me back or if I should consider a completely new pc.

Thanks in advance for any input!

[Lathais]

Even if you had a Motherboard that only had PCIE 2.0 you'd be fine. They are backwards compatible and really the only advantage of 3.0 is more bandwidth. Really, except for high-end cards in SLI, cards will not fill the bandwidth of 2.0, so 3.0 is mostly irrelevant.

[Nellah]

Even PCI-E 2.0 8x still provides a sizable percentage of peak performance in this price range for that matter, especially if you nab the 6/8GB version of whatever GPU you get, which at that price range will be the GTX 1060 / RX 480. You (OP) have 3.0 x16, which is still top end as PCI-E 4.0 hasn't come out yet AFAIK.

PCPartPicker lists the RX 480 4GB GPU as the best sub-200€ graphics card; bumping it up to sub-250€ gives you a choice between the 1060 6GB and the RX 480 8GB, which trade places on benchmarks depending on game and driver version used. Either one of those come in just under 60fps at 1080p Ultra in ME:A according to Kotaku, so dropping the details down a notch should average /minimum north of 60fps. Granted, their test was with a 4.9GHz i7, but the GPU comparisons still hold.

Both are leagues behind the GTX 1070, which (again according to PCPartPicker) start at 415€... a large price bump, but a similarly large performance boost, averaging 80fps at Ultra 1080p and widening its lead percentage at higher resolutions. If you are okay with paying that much for a GPU it will hold its high performance levels much longer than the 1060/480, and would be my recommendation if you intend to keep your GPU for at least three years.

EDIT: Though I don't really recommend "hardcore overclock" to open up a bottleneck, that 3570K can probably take some decent clocks if you have an aftermarket CPU cooler, which may help with newer games that are coming out. That said it's a perfectly fine CPU and should hold you through a few more years; there are few games that it will truly bottleneck: based on Ryzen reviews GTA5 and Battlefield 1 might choke it a bit, but other games should be still near optimal performance especially if your target is 60fps.

[Triggered Fridgekin]

I would honestly take some of your budget and invest in a decent heatsink for your 3570K, push it to 4.4ghz, reinvest in a case with great airflow if yours doesn't, an SSD and dump the rest in to a 1070. Aside from cleaning your filters you'll likely never need to see your tower again for another two or three years at which point you can skip most of this nonsense Intel has been pushing and will likely have AM4+ revisions by the time you need a new tower.