You can go straight from HS to Catalina.
Click on this link to read how to get different versions of macOS - https://support.apple.com/HT211683
- Make sure you have more RAM (memory) than what is noted as "minimum" for any particular system or your computer may run slowly.
- You may find you need to use Safari to get links for High Sierra and later using the Mac App Store application to open a functioning page.
- Upgrades may take some time (up to an hour or more) to install, with restarts and blank screens.
Before upgrading, back up your data in case something goes wrong. See this support document: Back up your Mac with Time Machine - https://support.apple.com/HT201250 or use a cloning tool.
Check if your old apps will still work with with the OS you want to install - https://roaringapps.com/apps This is particularly critical if you are upgrading to Catalina or newer, as older 32 bit apps will no longer work. To check for those, try this 32 bit application scanner application --> https://www.stclairsoft.com/Go64/
If you have a bunch of old devices you may well find that drivers may no longer work and Catalina versions are not available. You will have to check each one and see what the vendors have.