You do have to buy the update, it's not free, but it will upgrade your software to 10.3 (or 10.4 if you buy the latest) without you having to reinstall your applications software. You'll want to run Disk Utility (or DiskWarrior) and repair your permissions on your drive before and after doing the update. Just because your applications are still there, doesn't mean they are compatible with the new OS. You'll want to check with the manufacturers to see if they have any required updates. Also, do the Apple software updater after installing to see if Apple has released any minor updates as well.
P.S. Many people prefer backing up their current drive (always a good idea - either way) and then wiping the drive and reinstalling everything from scratch. It is not required, but makes for a cleaner system with a lower chance of problems occurring. Up to you which way you go. I've had good luck both ways.