What edition of Windows 7 do I need to allow me to VPN in to work?

Windows 7 Home Premium should be fine, since I believe all versions of Windows 7 can connect to a VPN natively and Home Premium comes with RDP to make those connections. What you should do though, is check with your IT department and make sure that their VPN software works on Windows 7. If they use Server 2003/2008/2008 R2 Routing and Remote Access no software should need to be installed and everything should work without any problem. If they use something like the Cisco VPN Server they currently do not support the Cisco VPN Client on Windows 7 64-bit. (Cisco VPN Anyconnect supposedly does)

As Peter said, Home editions cannot join a domain. I do not know if that will be an issue, but it is something to discuss with IT. Most companies don't require a home PC to join the domain, but yours might.