Large company I work for allows Keepass. I been in IT for 20+ years and haven't found an issue with it. Use it at work and at home.
Keepass is the bomb for personal passwords, especially those that are for highly sensitive accounts, but you need to have the mother of all passwords or a hardware encryption device like a yubico to protect the database. The mobile version is rather difficult to use, and nothing syncs without moving files + a manual import.
Pleasant Password Server is a network app that was built on top of Keepass. It is essentially a private, although typically corporate, form of online password servers.
When available, the best option is to use a Microsoft, Google, or your Amazon account setup with MFA to login to a site. MS and Google are doing well with their authentication apps to really cut down on password usage. I assume Amazon will follow. MS is ahead of the game as you can now use push notifications which only requires you to tap Accept on the phone when logging into something.
After that it really comes down to who you want to trust. For non-critical sites you can use pretty much anything, including auto-sync services from Google or TrendMicro, and online storage services such as Lastpass. For financial stuff, MFA is a must IMO and if it is not available there is no way I am putting the creds on someones cloud instance. Sure they are secure and someone is watching, but when the inevitable happens you won't be notified that it happened until months later. Even a good remembered password plus MFA (authenticator app or hardware token, not SMS or email pin) is better than some badass password.
As far as leetspeak, that shit is old and over with. Crackers have been incorporating the substitute characters for years. The best passwords are phrases (partial or full sentences with punctuation and proper camel case) that are corny (hard to guess) but mean something to you (easy for you to remember).