Getting a Thai DL was next on the list, but perhaps I should have done that before attempting the bank account, since the DL seems quite easy to get. However, I was foolish enough to apply for a residence certificate with the sole purpose of making a bank account, and I am still awaiting that one, so I am not sure if that residence certificate will be valid for the DL as well, or if I need to apply for a new one that states the purpose of the DL. At the immigration office they told me that a RC needs to be made again for every different purpose, but that might not be entirely correct.
I hadn't looked into getting a yellow book yet, but that might be a good idea as well.
I also heard that some people got bank accounts on the ED visa through their language school. Some schools seem to have a link with specific banks. However, I am not sure if the bank account can also be created for people at the school who are not on the ED visa.