There are many good password managers out there. One thing that would be a contributing factor is what devices you want to use the password manager on. If you re using Windows or Mac then most password managers will work there, but if you re also going to be using it on, say, Linux, then your choices would have to be pickier. LastPass is a popular option and the great thing about it is it has a website that can be used to access all your passwords and they have browser extensions for most popular browsers and even some less popular ones. Because they also have a website, you could always use that and manually copy/paste your passwords if you needed to, like on a public computer. I like how it s not based on an actual app on your computer, but rather your browser which gives it greater compatibility than any other password manager.
Another good option is KeePass. It is (in the theoretical sense) more secure/private because you are in full control of your password database. They generate a file that all your passwords are stored (and encrypted) in and because that database is like any regular file, you can keep it wherever you want (in a cloud storage, on a flash drive, or even just on your computer s hard drive). Although this is great for security and privacy, you need a KeePass database compatible app (there is not one specific KeePass app because anyone can build an app to work with KeePass databases). For Windows, Mac OSX, and Linux, I d recommend KeePassX. It offers a lot of functionality and is free and easy to use. For Android, I use KeePass2Android. I m not familiar with IOS but I m sure you can find a good KeePass database app for IOS, as well.
As far as Avast goes, I might recommend getting a different antivirus (if you re using Avast already), but nonetheless, I think their password manager is not necessary as there are many better and free alternatives.