Hi, this has been asked before a while ago so I thought I'd link you to what was answered back then to get you started:
https://news.ycombinator.com/item?id=13298195
I give a vote for 1Password on Mac but on Linux I quite like Pass.
Try Avast Passwords: https://www.avast.com/passwords
It is free and it covers all platforms (Windows, Mac, iOS and Android). Even synchronization between devices is for free.
I have around 100 accounts saved in my password manager so it is impossible now to be without passw. manager. I'm using SaferPass > www.saferpass.net
Yes, use a password manager. Unless you're a password savant that can remember every character he's typed, you'll either be re-using passwords (a big no-no), or storing them somewhere. It's much more secure to remember one strong password and use randomly generated passwords everywhere.
I use Lastpass. They have synchronization across devices on their free tier, which is awesome. You can automatically import passwords from Chrome or Firefox. They even have a "security challenge" that will show you what repeated and weak passwords you're using. Lastpass also has some degree of automatic password reset on popular sites, which works pretty well.