Wouldn't you have to update your VM constantly to keep up with your own changes?
Only if the changes are something you need to use in the VM. The idea of using a sandbox or a VM for what you are doing (web site access) is that if you get malware, you just blow away the VM and restore an uninfected copy. You update the browsers in the VM, and then save another copy of it. If you are using the VM for other things also, then you would need additional updates.