Do I need a password manager, and do I have to pay for one?
Answer first
It is worth it for almost everyone, but you do not have to pay. Your browser has one built in, and for most people that is enough.
A password manager makes it easier to use a unique password for every service. A password leak at one service then does not directly open your other accounts.
The program creates and stores long passwords for you. Protect the manager itself with a strong master password and two-factor authentication when available.
Your browser’s own manager is enough for many people. It is free and helps avoid reusing one password across different services.