This is a tricky one. SimpleHelp doesn’t do patch management. They focus more on remote access.
For patch management make sure when looking, look at exactly what 3rd party programs they support. Not everything is usually covered, so make sure they cover the apps you want to check/update. I have heard that https://www.tanium.com/ does well at patch management, windows, and third party, but I have not personally used them.
I also like PDQ inventory and deploy https://www.pdq.com/, but it is based more per site than if you have a bunch of clients from different locations. Let us know what you choose.
If you want to stick purely with simple help for an all-in-one solution, it will take a bit of work scripting things out through Powershell.