How to make sure apps remain available after upgrading macOS?
Generally, no separate action is required with respect to apps when upgrading macOS. All the installed apps and user data continue to remain available post upgradation.

However, it's important to ensure that the apps are compatible with the upgraded version of macOS before actually performing the upgrade. This information can generally be obtained from the vendor/developer of the app. 

There may be cases when upgrading macOS will also require you to upgrade the version of the app and associated licensing costs (if any). These all questions could be rightly addressed by the app vendor/developer.

On an important note, Apple advises to perform a system backup to guard against rare circumstances, where the upgrade goes wrong.

In your specific case, consider checking what's the latest version of OS X/macOS the machine can run. It might not go all the way to macOS High Sierra if it's too old. Obtain that information and plan your app update strategy accordingly.

Also, you should consider testing restoring your system from the backup to ensure its trustworthiness. People really don't want a backup - they want to know they can restore and the restore works. The backup is just the preparation to do the restore. You can run an erase/install and just reinstall the current OS to test things without the new OS potentially breaking things. That way you know you can restore the current OS first before you even think of upgrading.


How to reinstall macOS


It is worth emphasizing the should test since Mac OS X 10.6 Snow Leopard is really a long way back and it's very likely many of the apps will fail on macOS Sierra 10.12 or later and need license keys, upgrades, etc. Having a bootable backup or clone might even be worth the effort. You are about to break lots of things and gambling that they are all minor or not used since tons of functions and features from 10.6 are changed/deprecated/turned-off now. Any one upgrade alone, generally is easier to risk without a test run, but this is decade of neglect in terms of keeping things moving on the routine update/upgrade chain.