The choice of your Active Directory Domain name is entirely up to you. Its common to use the name of your company, or department of the company, but its not rigid. You can use an extension for the domain (.com, .net etc), however it is common practise to use the .local extension as this makes the domain distinct from internet based domains and non-routeabele.
Connecting workstations to a domain is done by right clicking on my computer, going to Compuer Name and setting this to the domain. In Vista it is in the system pane.
Setting up a correctly configured AD domain can be a complicated process, you need to ensure your DNS is setup correctly, user accounts are setup etc. I would suggest you do some reading, and setup a test environment to experiment with before you go live with your changes.
An excellent begginers guide to setting up AD can be found here
As for the VPN, using a VPN through the router has some advantages, its not dependant on any of your servers and will give you access to you whole network by default, however it needs its own authentication accounts (unless you use RADIUS), where as setting up a VPN server on your domain could then use your active directory accounts.