Welcome to the world of upgrading! These days, both Operating Systems and applications are regularly updated to keep pace with progress.
'Not upgrading' has the advantage that you reached a static point where everything works (or at least has fixed, known bugs). The problem comes, as you've found out, when you want something new, and it requires a newer OS than yours.
Upgrading 'one big jump' from very old software is more difficult than just 'the next version', because the change is so much larger. You will almost certainly have to update all your apps to match the OS, so you should check that there is a version compatible with the latest macOS (Catalina) for each one.
The good news is that any company still in business is likely to have current versions. Apple, as you would expect, has current versions of KeyNote, Pages and Numbers. Dropbox and other cloud services all have current versions.
The bad news is that some companies may require payment for newer versions.
There will always be unresolved bugs in any OS. But now is a good time in the 'annual cycle' to update, as Catalina is on its sixth and final release, so it's as good as it's going to get.
You should always download from Apple and nowhere else. Apple does make it difficult to obtain 'non-current' versions of the OS. This article provides links to some earlier versions on the Mac App Store.
If you have any software that runs as 32-bit binaries, with no updates available to 64-bit versions, then you may prefer to run Mojave (10.14) instead of Catalina. Catalina can only run 64-bit executable code, and won't run older 32-bit code.
If you do have old apps that don't have upgrades available, then you have two options: either use a separate volume with the earlier OS and boot to that when you want to use those apps; or use Virtual Machine software, such as Parallels, VMWare or VirtualBox, to create an 'OS within an OS', where you can use the older software.
Generally, it's best to keep up (to some extent) with new versions regularly. You don't always have to be on the very latest: you can be '1 year behind', for instance. But keeping up ensures that you receive important security fixes, as well as bug fixes; and that you don't fall behind into the situation you are now in.
It can be a bit of a pain when every time you launch an app to do some work, there's an alert that a new version is available: do you want to install it now? But it's good to set a small amount of time to deal with 'software admin'. Some apps (and those from the Mac App Store) can be set to install silently in the background.
Relying on software that is not being maintained is not a great place to be. Old, unsupported software will require old hardware, which eventually break down and become hard to repair or replace.