As for paying for services such that "customer of this VPN provider" can't be linked to you, I'd look at places that specifically accept bitcoin (I'm not a fan in general, but in this case, it signals their willingness to avoid collecting normal billing data like name, address, cc#, etc.).
I have no affiliation but they popped up in the googlings. Seems to be simple enough to get their service without giving away anything personally identifiable.
EDIT: the reason I tease out those two parts is because I'm concerned people will think TOR can protect against entities that can do a global customer-of-VPN dereference. TOR doesn't protect against global super-adversaries, consult your local security practitioner before feeling safe, etc. etc.
At the moment if I start up my VPN client and wait for the connection to my very trustworthy VPN provider, and only then open to Tor Browser Bundle, is that the right way round?
Thanks for the clarification.
TorrentFreak did a really good comparison of them recently: http://torrentfreak.com/which-vpn-services-take-your-anonymi...
Second, "no logs"... well: https://www.bestvpn.com/blog/8383/earthvpn-user-arrested-cop...
Good luck with your "no logs" operation in any NATO member/friendly country. Not sure about Russia and its allies, but I expect you'd be hard pressed to achieve "no logs" in China as well. South-Africa and Israel is probably out too. Not sure what that leaves you.