I am wanting to host a clan teamspeak server along with some of the websites I run. Is it possible to run a Teamspeak server off of a VPS? I have never used a VPS and dont know basically any of its cabablilities.

Yes, you can since you have root access.

Yeah setting up a TS server on any account is fairly simple. It takes a bit to make sure it starts back up when the server reboots, but nothing to hard.

I see no problem for you to go for a VPS. Perhaps posting all your concern to your future host could enlighten your decision, at the same time testing out your future host's ability to handle question.