Hello Bob,
Thanks for your interest in our VPS servers.
To answer your questions:
1) If you purchase a VPS plan with the same control panel you are using now on your basic plan, we will most likely be able to move your files and content over for you at no cost, otherwise there is a fee charged for the amount of time it takes.
If you wish to move everything yourself, it is pretty much how you described. Once everything is moved you would change the dns for the domain(s) and once that propagates (usually 24 to 72 hours or less) the site should resolve to the new location.
2) it is possible to open a port for the Teamspeak server on our VPS servers. It is easier on the newer Xen servers (which I would recommend for this) compared to the other less dedicated type Virtuozzo VPS servers but I am sure it can be worked out for you. You can see all our VPS plans here:
http://www.lunarpages.com/virtual-private-server/.
Feel free to ask any other questions you may have.