Good afternoon. I have an Orange Pi One and I need to achieve the maximum boot speed. The ultimate goal is a kiosk mode and the only application on the QT. The network is not needed.
The simplest way will probably be to change the run level to the single mode, but with this there are problems.
Any tips, suggestions, experiences?

You could try buildroot, which has boot times at around 2-3 seconds. I used armbian's build system to help build a working kernel that has all the stuff you're used to (USB OTG, ethernet, GPIO, etc). It is totally customizable for which packages you need installed, and its got the fastest boot I've seen. Which applications do you want on the device? Do you mind if its mainline or legacy?

An application on a QT that manages some device. Legacy kernel. I'm aware of the buildroot, but I'd like to use armbian and use the ubuntu repositories. Maybe there is a way to set up the armbian and configure it correctly? If not, I will use buildroot. 

Why not look at your boot process first? You could start by running systemd-analyze blame and see what takes how long on your system to boot... systemd-analyze can also plot nice graphs of your boot process...

 

http://pastebin.ubuntu.com/24916964/ for example output from my Thinkpad

 

Further running  systemd-analyze critical-chain gives you hints where your boot process is delayed the most...

 

https://wiki.archlinux.org/index.php/Improving_performance/Boot_process