It's something I always have never been quite sure about... I usually go with drivers first, updates and then programs, but maybe it doesn't even matter at all...
Updates before drivers, because if something doesn't work it might be an outdated driver that is already installed, and an update will fix it, whereas downloading a driver from the internet might cause a conflict with the currently installed one or with your hardware if you download the wrong driver.
Whenever I install a new operating system my monitor's resolution is all messed up, and by updating the system the driver gets updated and the resolution adjusted. On the other hand I see a lot of questions here from people with fresh installs that download proprietary drivers on Linux as soon as they boot the system and see that something isn't working, like the display's resolution. The proprietary driver just makes things worst, since the free one was just outdated.
As for applications... I'd install them after everything else since it's the least important part in a "getting things working" point of view. You can install them first, but some might not work with an outdated system (unlikely to happen).
Windows update has allot of hardware has drivers available trough Windows Update optional updates section. So by running it first manually and checking the optional section you can usually get both updates and drivers in one go.
But answering your question, drivers or lack of proper drivers can seriously impact a machine performance or even make it "unusable" such as lack of ethernet or hdd drivers, so starting with them is always a good idea. OS updates come as second most important as they fix bugs which can cause all sort of problems.
So i'd say you're doing the most logical order to minimize potential problems, however I'm not convinced doing the inverse order would cause issues on the vast majority of cases.
About six years ago I had a Dell laptop, and after a fresh install there was no network, because of missing drivers. So first thing was to download drivers on another computer and install them. In this particular case (several identical company laptops) I kept a folder on my harddrive with all drivers that should be installed right after installing Windows.
If you know that drivers will not be installed with Windows, then install them right after installing Windows, because of missing functionality like screen resolution and network. Zip all those drivers and back them up!