You might want to dedicate a few hours one weekday to accomplish this. You will want to open your account sooner than later.
Note: The fun thing about this process in Spain is that not only will each bank require something different, but each branch location might as well. Sometimes even employees at the same location ask for different requisites!
Requirements for opening an account:
Valid Passport
NIE (Foreigner Identification Number)
Local Address
Spanish phone number
TIE card (physical ID card) (varies on the bank)
Employment contract (varies on bank)
⚠️ Some banks will tell you that you need to buy insurance from them in order to open an account. There is no need to pay for this. ⚠️
Other banks will tell you that they will not be able to open an account without a physical TIE -- if they tell you this, don't worry, just try another bank.
Eventually, you will be able to open an account with just your passport or (passport + NIE). However, you will probably have to return to the branch afterwards to show them your physical TIE card after you've collected it.
Some Spanish banks that allow foreigners to open accounts with a passport include:
Sabadell
BBVA
Note: Please bear in mind that this will be part of your To-Do List/Steps when going through the process. It will then be explained again.