I would like to do the complete installation without screen. It would be good if I can use it like a virtual machine or I could connect to it like a remote desktop.
The most straightforward way would be to piggyback the x86 world of PXE booting, presumably with something like ipxe.org. Unfortunately, PXE boot is not implemented on ARM systems, at least not the Pi. Oh, and iPXE on ARM was definitely not on the roadmap back in 2011, so that probably won't work. So, that really only leaves CoreOS and Docker on the Raspberry Pi, but that assumes you want to use the Pi for something other than desktop support. CoreOS and Docker are definitely happening, but that is still a pre-built system that just happens to be relatively flexible afterwords.
If what you want is to have a Raspberry Pi preconfigured, then search around for methods to replicate (micro)SD cards with validated images at a scale that meets your needs. Less than a dozen a month = do it by hand. A dozen or more a day = buy a duplicator.