I agree on the paper note if it is purely about safety, but it has happened too often that I’m away at the University, or traveling, and I need a certain password to log in on a different PC.
Of course there are only few passwords for which a ‘reset password’ button is not an issue, but even those are more difficult to remember than one long, secure sentence.
And for the others I just do not want to go through the whole password reset e-mail processen every time.
So for me, a good password manager is the best option. I use LastPass since it was recommended by security experts when I was looking for a password manager and it is free (there is a premium version so their business model is solid). I have it on my phone, and as a browser extension in all major browsers. I have been using the free version for years now and can highly recommend it.
And in the end, a good, encrypted password manager with a long password that is only in your head is not only more comfortable than a piece of paper with just the critical passwords. It is also safer.
PS NEVER REUSE PASSWORDS!
That is really the most important thing and for me, that is only doable with a password manager