I absolutely need a new laptop, since mine is already about 10 years old and accordingly also mega lame ^^
Since I'm not very familiar with laptops (in terms of performance, etc.), I wanted to ask what you think of this?
You won't have much joy with a laptop for 200-300 euro, especially if you want it to be a bit faster, I would invest more.
Well, there are already good used devices for it
I would buy a used one for your budget. On Ebay small
Ads or Ebay are offered in bulk.
At the price, I wouldn't even think of new devices.
If you also find used devices in order: There are e.g. Thinkpads with i5 (5th Gen upwards, 8GB RAM and SSD) from 200 euro…
What size would you like? 12 ", 14", 15 ", 17"?
Between 15 and 17 inches is fine.