Graphics Card / Motherboard Compatibility

Hi, to keep it simple, a graphics card connects to a PCI type port.
The standard today is PCIe and your motherboard has two ports (2.0 though, some recent graphics cards need 3.0 so be careful), so you can use any recent graphics card compliant with the PCIe 2.0 standard.
However, I see that your motherboard format is Micro-ATX, so if your case is the same size, you'll need to be very careful not to choose a graphics card that's too large for your case! (or the easy solution, change the case to an ATX)

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Hello,
your Asus P8H67-M EVO motherboard is recent enough to support all current graphics cards, there shouldn't be any issues

I have a 500W ATX power supply
now, I'm not sure if that's good or not, I need to know the brand and model of the power supply please
it would also be good to know your CPU, because there's no point in suggesting a GTX 970 for example if you have a Pentium G

finally, last question:
is your case big enough to accommodate any graphics card?
if it's a commercial model, please provide the brand and model
because Darskater's comment on your micro-ATX motherboard is well noted ;)

Thank you. For the power supply, I don't have any other details on hand (I am in Mulhouse and the PC is in Brest... I know, it's complicated).
For the case, no worries, it's a standard tower, neither mini nor maxi...
The CPU is an i5 2500@3300 MHz (max: 3811).
Thank you for any additional information you can provide with this info.
PH.

Just like that, just passing through...
Is there no problem installing a graphics card with a PCIe 3.0 on a PCIe 2.0 BUS?
I'm asking this just because, since all the cards on the market right now are 3.0...
PH.

Without knowing your power supply, it's hard to advise you for sure

your CPU is very good, so any graphics card will do, and since you have a standard case, you won't have any issues installing it

I forgot to ask what screen you have, if it’s at least a Full HD (1920 x 1080), or even 2560 x 1440

If so, with your large budget, you can go for a GTX 970, which is around 360€, assuming you have a branded power supply (Antec, Corsair,..., otherwise you'll need to change it):
https://www.materiel.net/produit/201409160254.html?affcode=clubic&utm_source=clubiccom&utm_medium=comparateur&utm_campaign=Composants+PC&utm_term=GeForce+GTX+970+Gaming+4G+-+4+Go
in terms of performance, it's close to an older generation GTX 780 Ti, while consuming about 10% less
you can read its review here:
https://www.hardware.fr/articles/928-1/nvidia-geforce-gtx-980-gtx-970-gm204-maxwell-gigabyte-g1-gaming-test.html

Is there any issue installing a graphics card with PCIe 3.0 on a PCIe 2.0 bus?
no, it’s fully compatible, only the maximum exchange speed between the CPU and the graphics card is reduced, which is rather imperceptible in games currently:
https://www.hardware.fr/articles/850-4/battlefield-3-crysis-2-civilization-v.html

OK.
Thank you very much for all this information.
PH.

Just for your information: I found the exact reference of the power supply
namely: LDLC-BG-500ATX12V-500W FAN12CM
The question that arises given this information is: is it really necessary to change the power supply if I choose the aforementioned graphics card?
Thank you.
PH.

Is there anyone left?
PH.

Your power supply is suitable for your new setup; it's actually a Seasonic.

OK. Thank you very much
PH.

Another stupid question. I know, I'm annoying...
What are the two "weird little pins" on top of the Asus GTX 970 card for?
It seems like they should be connected to something, somewhere...
But what and where?
Thank you.
PH.

Hello,
are you talking about the 2 gold-plated connectors that we see at the bottom left of this photo?
https://images.bit-tech.net/content_images/2014/09/nvidia-geforce-gtx-970-review/asus970-3b.jpg

If so, they are the connectors for SLI (connecting 2 identical GPUs together for more power).

That's right.
Thank you for your response.
PH.

What should I connect to my screen? DVI? VGA?....
PH.

Hello again!
I'm back at it!!!
I finally changed my graphics card to a "GTX 970".
The problem is that now my CPU (Intel Core i5) is overheating and everything shuts down. Where does this come from?
And most importantly, what should I do?
Thanks for your answers.
PH.

Hello,
it's hard to be sure from a distance
it could be a fault with your cooler
it could be an overheating issue with your case

give us your temperatures with HW Monitor

we don't know your cooler:
what is it? brand and model please
nor your case:
brand and model, how many fans installed?