You want to use baremetal (ESXi, Xen, Hyper-V, and somewhat KVM). Virtualbox is a great tool... but the fact that it depends on the host OS makes it a very poor choice to have servers running on them. If you are looking to virtualize your router, then you definitely want that to be baremetal.
You want the servers running on a very stable platform. It's not that Virtualbox is the problem... but the host OS. I'm going to assume it's Windows here, and we all know the stablitly of Windows is not as reliable as we'd like.
When you run a baremetal hypervisor, the platform is extremely reliable, and very stable... so you always have the ability to connect to and service your VMs. In the case of Virtualbox, once the host OS goes... you have just killed every VM running.
I've used all the major hypervisors, and ESXi, even the free one, is the most capable and simple to get going.
I've currently settled on ESXi 5.1 update 1, as it has the best driver/device support for consumer level hardware. It runs from a USB stick on an AMD 8 core 8350 CPU, 32GB of RAM, and an ASRock Extreme4 mobo. I can pass-through nearly any PCI card, and I do pass-through an IBM M1015 raid card with 8 hard drives to a VM to serve as my NAS. Then I pass through a couple of NICs to run a virtual router for my internet service. Those two are my "critical" servers. Everything else is dependant on those two VMs.