There are a ton of possibilities here that could make a very big difference in how you would set things up if you were putting the machine(s) on both networks.
First and foremost, read your company's policy about hooking their network to other networks. If you do this - even through a dual-connected machine - you may be risking your job if a security issue arises.
If your work machine will be using a VPN package, it is likely that they will also use a firewall and shut down or prevent any sharing of any other network arrangement on the laptop when it is VPN'd into work. This prevents you from effectively using your networked printers to avoid the security risks. You could locally attach your printer to the work machine.
If they are cavalier about security and allow you to hook the machines together or have a dual-connected (multi-homed) machine, then it will be up to you to enforce any security you want to by making your personal machines and the office machine secure from each other. You should NOT enable routing of one network to the other at any time.
I don't recommend hooking them together, or hooking the networks together. There are just too many risks and in some cases you will run into issues with some software due to the multi-network arrangement.
Instead, get a docking station and KVM for the laptop and your home machine. You can hook those up and easily switch back and forth between machines, but still maintain separate security and network integrity. And no job loss threat, either!
