(*) - The layer 2 or MAC address, only can be important to a local netowrk or to a ISP.
Maybe to startup, you can execute a tool, that close a tunnel SSL to another network where you can browser, how for exemple
- Hotspot Shield
- Super Hide IP
Also is possible try use a project "Whonix" that use the network Tor.
Depending on the purpose of concealing his identity in the navigation, you can search for a wifi with wep to be opened or seek people with superpowers cow le grant access to underground through some ISP.
A virtual machine can easily be changed through the mac address of the virtual machine configurations. A Linux box too.
Recalling that a mac address contains the first octet information for the manufacturer, so it is advisable to change this information prudently.
For example if you use a virtual machine to navigate through the site on a local network, can quickly identify the machine by mac because virtual machines have this identification in the first octet, so it might be interesting to change the MAC to confuse an administrator who is identifying this source, perhaps with a mac spoofing.
I have a good imagination, I speak only for study purposes.