Have you try with DHCP server?
•In the VirtualBox graphical user interface, you can configure all these items in the global settings via "File" → "Preferences" → "Network", which lists all host-only networks which are presently in use. Click on the network name and then on the "Edit" button to the right, and you can modify the adapter and DHCP settings.
EDIT:
As you are trying to establish connectivity between host and guest, and need guest to have internet connection, I think your best option is to change from two adapters (host only Adapter and NAT) to only one adapter on bridge adapter mode.
When you setup a "host only Adapter" you need to change your host IP adress to make connection between host and guest possible, this way host and guest loose internet connectivity as host and router are on two different networks.
So if you want to have internet connection on both guest and host, and connect with each other, bridge adapter is what you look for. This way your guest will be seen to your host and the router as another computer attached to it.
Anyhow a look at the manual will not hurt.