Theoretically, which would be capable of providing the highest level of anonymity, Tor or a VPN?
Unless you can somehow prevent your VPN provider from knowing who you are or what your IP address is, there will always be the possibility of your anonymity being compromised.
You could conceivably sign up to a service under a pseudonym, pay for the service using a bitcurrency that you had sourced anonymously, and ensure every time you connected to the VPN it was in no way traceable to an IP address associated with you. But given the other things you'd also have to consider - your online behaviour, locking down certain aspects of your machine, etc. - the hassle of this, and the risks of making mistakes, then makes VPN an increasingly unappealing choice.
From the Tor FAQ:
VPNs have a single point of failure: the VPN provider. A technically proficient attacker or a number of employees could retrieve the full identity information associated with a VPN user.
Using both a VPN and Tor together is another consideration, which has been discussed in plenty of other questions.
Tor will get you on a "list". If you connect to a Tor node and that's it, your ISP knows you are using Tor. They won't know your traffic but they will know that you're on Tor. I personally would get a VPN based in the Netherlands or somewhere they don't have to keep logs. http://www.cnet.com/news/nsa-likely-targets-anybody-whos-tor-curious/
Also, a group of hackers worked with the NSA to "crack" TOR. Its compromised and thats one reason why I don't use it.
Like the person above me said.. VPN's have a single point of failure.
My answer is VPN to Tor. Your speeds will be horrid, but you'll be anonymous.