As a programmer I get a lot of people who ask me to recommend different things for their computers (most assume because I’m a software engineer I know everything about computers, too). While I’m no computer engineer I’ve been working with them for 20 years so I’ve learned a thing or two, probably more than your average software programmer just out of college might know.
A common question I get is about password vaults (online, computer-based or otherwise). While I always recommend people use multi-factor authentication (MFA) whenever possible, for keeping passwords I like LastPass. It has a lot of nice features for a free, online password vault.
The Premium version, which is only $12 a year, includes a variety of MFA for changing/accessing from your different computers, and can be used as an app on various mobile platforms (Android, iPhone, etc.). You can also then share links/passwords with other LastPass users even if they aren’t Premium users.
As always, do some comparison shopping to find what best suits your needs, but for what it’s worth LastPass is the one I like best.