Are they really trustworthy? Will I have them around? How do they work?
I use KeePassXC (paired with Syncthing for synchronization). It stores all your passwords in an encrypted file which can only be opened with your master password. Assuming you have a strong master password, this file can be sent around in unsafe places like e-mail or Dropbox. On Android I use KeePassDX. Most of the “KeePass” programs are compatible with each other.
Syncthing
That’s just for computers. How do you keep a computer and a phone in sync?
This is the problem I had with PasswordSafe. Two files.
They work very well together, though Syncthing is a little weird to set up at first. On Windows I use SyncTrayzor.
Syncthing is probably the safest of all options, but if you want to trade a bit of paranoia for convenience, you can also sync your keepass database to a cloud provider of your choice. Then your pc doesnt have to be running to synchronize. As long as AES stays secure, even the cloud provider cannot decrypt it.
For added security, you can encrypt your password database with a file in addition to the master password (and then manually transfer that file to your phone via wire once).
Bitwarden. Yes, very secure, but if you are extra tinfoil about it you can host a bit warden server yourself
Just use bitwarden it’s free and open source