A good privacy oriented VPN is a good start. Obviously I am partial to Anonymizer.com. TOR can work well, but I worry that many node operators may be sniffing any and all traffic in the clear.
I suggest using virtualization. VMWare or Virtual Box can give you a disposable environment that you can reset after each use. That provides a lot of protection, in conjunction with the VPN.
As to trustworthy, it is hard to say. One can't really prove a negative. Look at the privacy policies to see that they at least SAY they don't keep logs. Then look for cases where users have been compromised. That almost always gets out. Hide My Ass was shown to keep logs when it lead to the arrest of a member of LulzSec.
Having founded anonymizer.com in 1995 and being actively involved with it to the present day, I have some first hand experience with this issue. Our business and servers are all located in the US, so this may not apply in other countries.
Over the years the number of subpoenas we have received has varied significantly, but has never really been less than several per month. As we have no logging that would connect our users to their actions, we can't be responsive to that kind of request. As a subscription service, we could be (and have been) asked if a given person is a customer, but that would not say anything about what they had done.
We have been asked to set up ongoing monitoring that would allow us to capture this kind of information, but we have declined, and no legal force has been brought to bear that could force us to do so.
The real problem is that your computer and browser are probably so well profiled, and full of tracking elements, that you are likely to be identified even while using a privacy VPN, unless you take significant additional steps.