Memory as option #1
Paper and pen....and a safe when option #1 fails.
100% secure.
My memory started to fail when I around 70-80 logins or so. That was a LONG time ago, when service providers didn't enforce very stringent password requirements (short 6-8 characters, no special characters/numerals needed, no password expiration, reusing passwords acceptable). Today many organizations enforce stricter rules: 8-16 characters, at least one special character, numeral or uppercase letter, no password recycling.
For sure, you don't want to use the same password at every site, but these days, it's impossible to do so since each site operator has different password requirements. Things like, did I throw in a capital letter on Site A or did I replace the letter "i" with an exclamation point on Site B, or did I add another character because the password was too short?
Writing them down isn't safe nor secure. And often isn't convenient either. The piece of paper could get destroyed or viewed, if you stuck them in a wallet they could get lost or stolen. If you kept them at a desk, they wouldn't be available on the go.
I now have 500+ logins/passwords; it happens when you've been on the World Wide Web for 20+ years. A piece of paper with five hundred logins/passwords would be hard to read and search. If I signed up for AirBnb today, I would likely have to put them at the bottom of the list. Two years from now, where would I start looking for the AirBnb login credentials on that piece of paper.
Before I started using a password manager app, I kept my logins in a text file on my computer. At least I could insert/delete logins and keep them alphabetical, and I could search on the document. Procedures like encrypting the file are inconvenient (like using PGP).
Today's modern password managers like 1Password, LastPass, and others are far more convenient and safe than trying to remember 500+ passwords (I can't) or writing them down on a piece of paper. Plus, many sites will have you set up security questions, again something that a piece of paper doesn't handle well. Not a problem for the database-backed password managers like 1Password.
Worse, paper deteriorates. What happens when your sheet of paper starts to crumble? Do you rewrite all of your logins on a new sheet of paper? Do you realphabetize in the process? What happens if you forget one and it doesn't make it to the new sheet of paper?
Unless you use a more advanced system like a card catalog, writing login credentials on a sheet of paper does not scale well. Either way, you still have to worry about damage, theft, and convenience.
Plus, password manager apps often accommodate other data. You can have things like WiFi router logins, credit card numbers (including CVVs, expiration dates), driver's license, passport, auto insurance policy numbers, reward program IDs, bank account numbers, and more. It's up to you to assess the risk between between security and convenience and decide how much you are willing to put in an app and not lose any sleep.