I can share the config that I use. I am on a laptop and use wireless to connect to my network and use a bridged configuration so that my guest OSes can be on the same network as the rest of my computers.
Adapter Type: PCnet-FAST III (Am79C973)
Attached to: Bridged Adapter
Name: Dell Wireless
The "Adapter Type:" is the adapter that will be emulated to the Guest OS. "Dell Wireless" is my wireless interfaced as it is named in the Host OS. after selecting "Bridged Adapter", the "Name" list will be populated with the names of the interfaces available in the Host OS. I have also used "Attached to: Host only Adapter" on a second interface and also on a second VM to test the DnsMasq extesion I created (after turning off the DHCP server in VBox under the Network Preferences.) In another scenario, I have used "Bridged Adapter" and attached it to my VPN interface which puts the Guest OS on the VPN network.
In short, all network configurations that I have tried has worked for me. If you continue to have trouble, it may be worth re-installing VBox and ensuring that all the networking support is installed.