I recently moved from Berlin to the other side of Germany, Aachen, to begin my studies, but I wansn't able to move my desktop pc, I plan to do it after I find a fixed place to live. For the moment I need a cheap laptop (under €200), Is it a good idea to buy an old factory refurbished laptop on ebay or are there better options? Most of these laptops have 4GB RAM and an i5 3rd generation procesor and are between 170 and 200 euros.
They might be a little clunky, but for basic web browsing, word processing, etc they'll work. You could buy some more RAM, or potentially an SSD, to speed things up. Especially if this is a short term thing, it is doable.
Another option, are you comfortable with Linux? Most Linux distro's are significantly lighter weight and will run better on an old laptop.