You should use both if you are really concerned about anonymity. Using a VPN will conceal the fact that you are using TOR from your ISP, so there won't be logs showing you were on TOR. Some VPNs also keep logs, so you should do a little research and make sure to choose one that doesn't.
Also, if you are concerned about Big Brother, you should make sure that you choose a VPN that is NOT in the US. Otherwise, all those surveillance laws apply to the VPN and they are subject to subpoenas and National Security Letters just like any other business.