Storing passwords in a file on your computer is risky as any time that that computer might be stolen or offered to a tech support person because the computer won't boot, offers your entire collection to others.
Corruption of that single file destroys your ability to get to everyone of your passwords.
The inconvenience of having to access that file every time you need a password will cause laziness which will cause for that information to be seen by others.
Using applications, free or paid, will put dependencies on that program to work and be secure.
The rules for good, safe, strong passwords are that they be different for every destination. They should not be easily deciphered. The should consist of numbers, letters, and probably capitals, etc. They should be easily recalled so that they do not have to be written down on post it notes, files, or other places that can be found or damaged and become inaccessible.
Instead of using other outside solutions, look to those tools that you will always have with you and are very powerful. The best tool is your brain. If it is not available or working well, then use of the password is not really necessary. Here is how to use your brain:
Let's say that you need a password for the RealTown.com website. Your job is to create a 'system' that you can easily remember and apply to this unique site.
One idea for this suggested new method is to select a 4-5 letter word that starts with a vowel. Let's say it is 'apple'. Now pick a unique number. Let's say it is '23'. Choose to capitalize one or more letters in the word 'apple'. Your choice might be to capitalize the 2nd letter and let it become 'aPple'. Combine this with your favorite number. Your unique personal password becomes 'aPple23'. Use this password as your own personal password for your computer and other personal items. It will meet most every requirement for passwords that you will come across.
But now you need to address the fact that you need a unique password for every site and destination. If you are wanting to have a password for RealTown, one method would be to perhaps add 'rt' (for *R*eal *T*own)to your personal password which would cause it to become 'rtaPple23'. If you need a password for the New York Times web site, it would be 'nytaPple23' because you have prepended the initials 'nyt' to your personal password.
Variations on this theme would allow for you to instead perhaps put the unique site specific part at the end of your password, ie. 'aPple23nyt'. Or perhaps you might want to capitalize the 2nd letter of any sites acronym as in 'nYtaPple23'. Vary this as you wish but be consistent.
The specific methodology or formula that you use is not really important. What is important is that you have a system that is easily remembered or calculated in your head without relying on some outside aid that may not be available. You will only need to remember your personal password ('aPple23') and then simply append or prepend your site specific alteration which will be unique to every site you visit. The cost is $0 and this will be as secure as any other method.
Do always remember that you should not share your method with anyone other than those that are forever trusted. Kinda like my kids who know my scheme for access in case it might be necessary but also know that I would break their legs if they used it improperly. ;-)