Well there should be a sticker if you have a laptop. If you have a desktop, you can just open the case and take a look inside.
Try finding the model number of your desktop/laptop (which one is it actually?) and then search on the internet. Also if you found the model, please mention it here too.
And what are you downloading? NVIDIA or AMD drivers? Don't try any of them before you know for sure what graphic card you have.
Also, there are probably more places too download the drivers from but I only recommend these ones.
Anyways, your integrated GPU seems to be working fine with indeed Mesa. I do not understand why it wouldn't work for you.
Try finding the model number of your desktop/laptop (which one is it actually?) and then search on the internet. Also if you found the model, please mention it here too.
And what are you downloading? NVIDIA or AMD drivers? Don't try any of them before you know for sure what graphic card you have.
Also, there are probably more places too download the drivers from but I only recommend these ones.
Anyways, your integrated GPU seems to be working fine with indeed Mesa. I do not understand why it wouldn't work for you.