I frequently see discussions around which password manager to use. I personally use KeePass. This is an open source program that allows you to have control in your data. The database format is encrypted so as long as you keep your master password secure, the chance of someone getting access to your passwords is practically zero.
This document is just meant as a signpost to steer you in the right direction of how to set up KeePass across multiple operating systems and have your file synced in the cloud all while paying $0 and not having to set up a single server to do so.
You can skip this if you don't care
I use KeePass because it's free and not proprietary. There are a lot of alternatives out there such as LastPass, 1Password, Dashlane, and Bitwarden. A lot of these are subscription based which makes it a bit prohibitive for users that can't afford it. Bitwarden is free and open source, should you decide to host it yourself.
I believe security should be free for everyone, including those without the technical know-how to set up a server and those who don't have a credit card to pay for a subscription service. The earlier you use a password manager the better.
The .kbdx format is well supported by multiple clients. Luckily, despite being proprietary a lot of other password managers provide export such as 1Password's .1pux format. However, as far as I'm aware these file formats are unencrypted so they're not useful for secure storage.
The final reason why I use KeePass is because it isn't prone to data breaches. LastPass has had multiple data breaches. In the over 10 years I've been using KeePass, my data has never been breached nor have I ever been scared of it.
For desktop you have a few options. You can either download the original .NET KeePass program for Windows operating systems, or if you're in another operating system you can use either KeePassXC or MacPass if you're on macOS. Note that KeePassXC is cross-platform and works on all operating systems. If you frequently use multiple operating systems or if this is important to you then I recommend using KeePassXC as your client. Otherwise the native client of your choice is sufficient.
I personally use KeePass on Windows and KeePassXC on Linux.
If you are expecting to sync your data across multiple devices, it is recommended to have a cloud storage system to synchronise your file. There are multiple ways of doing this, but the ones with the widest support in the ecosystem are either Dropbox or OneDrive. Both of these work across all operating systems and have many clients. On top of that, the free plan is more than enough to store all your passwords. If you're in the Apple ecosystem you can also use iCloud which is supported by both MacPass or KeePassium. More on the latter later.
I personally use OneDrive because it allows more concurrent users for free than Dropbox. However, your mileage may vary.
If you use an Android device, the easiest and best way to set up KeePass is by using the KeePass2Android app. It supports all the cloud services I mentioned above (except iCloud) and works flawlessly.
Be sure to turn on the AutoFill Service for better ease of use through Settings > Password Entry Access > AutoFill Service and following the instructions there, if any.
My preferred app on the iOS ecosystem is KeePassium. It's free and integrates well with the operating system. It also supports all the popular cloud providers so syncing should be relatively simple. If you're only in the Apple ecosystem, it has support for iCloud syncing as well.