What GPU should I get for my Ryzen 7 5700G build within a €300-€350 budget?

For your budget, the 5060 is a solid choice since it's sometimes cheaper than the 4060. Just make sure you avoid the 4060 Ti and the 5060 Ti at 8GB, as they might struggle with your current setup's PCIe 3.0 limitations. Also, I'd strongly recommend getting a new PSU; the one you have isn’t very reliable.

You might want to check out a used 9060 XT with 16GB if you can find one in your price range—prices have been fluctuating a lot lately. But remember, your PSU could limit you, so that’s something to keep in mind. It would help to know what resolution and games you’re planning to play, as that can affect performance expectations.

Since your 5700G only supports PCIe gen 3, you might experience a loss in performance if you go for newer GPUs. The RTX 4060 might not be the best fit since you'll lose some frames compared to older models. If you're in the European market, consider the 5060; it's often cheaper and would work better with your setup. Also, definitely think about upgrading that power supply since it's not 80+ certified, which could be a problem even if you don't change your GPU.