I got some options like VHD, VMDK, HDD, and VDI
is there a file type that is most commonly used and is supported by most other virtual disk software?
VMDK will be supported by VMware, and VHD is used by Microsoft VirtualPC. You can get more information here.
VDI is the native format so it should be the ideal for virtualbox.
However, other forms allows compatibility with another system such vmware and "virtualpc"
Windows 7 and windows 2008 r2 is able to mount VHD natively.
It really only matters if you're planning to use the same virtual hard disk with another virtualization provider.
If you're only planning to stay with VirtualBox then it really doesn't matter. But I would assume VDI would be preferred in this case as it seems to be the native format.
Even if you plan to move to another solution later on. There are ways to convert between the formats.
1) If you first make the virtual machine on virtualbox and use virtualbox to add an Open Source or licensed OS and applications in the VM as an open source private cloud IaaP tool use VDI as the file type. If you plan to first make the virtual machine on virtualbox, use it on virtualbox to put licensed or unlincensed application(s) software on the OS and snapshot it and use it on as an example wmare then use VDI, export it via the Window Manager and convert it to vmdk. As stated above there are many ways and utilities to do the conversion. The conversion that is best depends on your platform(s) and environment(s).
2) If you first make the virtual machine on virtualbox and need to only put an Open Source or license OS on it with/without applications then export it to a IaaS environment private cloud then as an example for wmware use vmdk. Once it is made use the Windows Manager to export it in this raw original format. In this case there would be no need to convert the file for use in the wmare vdc virtual machine platform environment of the IaaS provider.