You'll need to define some requirements for seperating the networks.
Is your work computer provided to you by your employer so you can work from home? If that's the case, you should look to your employer's IT department for guidance on what you need to do.
On the other hand, if your work computer is something that you use for your own small/home business, then it's up to you to define what is required (unless your business involves some data that falls under a regulatory body...in that case, the regulations might define what you need to do to be in compliance). That being said, with a good hardware firewall in place between your work network and home network, you should be able to share a single internet connection. But, depending on your abilities, you might want to contract an outside vendor to set this up for you.