I am using Windows 10 Pro 1709 (OS build 16299.1087).
Windows 10 version 1709 End of Service (EOS) date was back on April 9, 2019. So if you want a stable system you should immediately upgrade to one of the supported versions. Windows 10 version 1803 will reach End of Service on November 12, 2019.
Windows 10 version 1809 and Windows 10 version 1903 will each End of Service on May 12, 2020 and December 8, 2020 respectfully. The next feature update (19H2) will be a cumulative update for 1903. This likely will result in an extension of the End of Service date to 1903 more than likely.
Since I use my PC professionally I want a stable running system.
Windows 10 version 1809 and Windows 10 version 1903 are both considered stable. The majority of the issues that were blocking users from 1903 have actually been resolved. Most issues that exist on Windows 10 version 1903 also are also a problem for Windows 10 version 1809 (outside issues specific to Windows Sandbox).
I know that there quality and stability issues with 1803 and 1809. So
my question is: Should I update to 1803, 1809 or 1903 to get the most
Those stability issues have been resolved for months. Windows 10 version 1709 has numerous issues that are open currently, so it's not like that particular version of Windows 10, isn't without it's own flaws. At the end of the day, most Windows 10 issues, apply the majority of the features. It's only when an issue is specific to a feature, that only exists within a single Windows 10 version, is a feature release affected by that issue.
I plan to go for 1809. As I mentioned in my question the system already downloaded 1803. How do I avoid the installation of 1803 and go directly to 1809?
You should use the Disk Cleanup tool to cleanup the temporary files, then download a Windows 10 1809 ISO, and perform the upgrade to Windows 10 1809 by mounting the image within Windows.