The whole "under" "over" "through" Tor is confusing. Better to say User -> Tor -> VPN -> Internet etc.
The docs and Tor Project seem to say that connecting to a VPN last in the chain before the Internet is bad and chancy.
Ego already said:
If the VPN/Proxy is the last part of the Connection, then a Server will not be able to determine that you Access it via Tor. Keep in mind though that under such circumstances, your ISP will know that you use Tor, though not in what way.
But, do you really trust that the VPN will never fail and be configured correctly to hide Tor use behind it?
Also, The Tor Project notes:
You can also route VPN/SSH services through Tor. That hides and secures your Internet activity from Tor exit nodes. Although you are exposed to VPN/SSH exit nodes, you at least get to choose them. If you're using VPN/SSHs in this way, you'll want to pay for them anonymously (cash in the mail [beware of your fingerprint and printer fingerprint], Liberty Reserve, well-laundered Bitcoin, etc).
However, you can't readily do this without using virtual machines. And you'll need to use TCP mode for the VPNs (to route through Tor). In our experience, establishing VPN connections through Tor is chancy, and requires much tweaking.
Even if you pay for them anonymously, you're making a bottleneck where all your traffic goes -- the VPN/SSH can build a profile of everything you do, and over time that will probably be really dangerous.
So, why is this bad?:
- VPN sees everything you're doing.
- VPNs can (and do) fail.
- The setup is hard and "chancy" according to the Tor Project.
- You don't evade network censor Tor bans.
- You don't hide Tor use from ISPs.
- You lose stream isolation.
- Your web fingerprint is worsened.
- You have a permanent exit relay.
- You can't connect to Tor hidden services.
- The anonymity effects are disputed.
So, just to reinforce that - difficult to set up, costs money (with probable honeypot providers), worsens fingerprint, removes stream isolation, will probably fail and reveal Tor use at some stage, and anonymity effects are disputed.
All in all, a terrible plan just to (maybe) hide Tor use from websites.
Re: "Other Browsers"
Don't use other browsers with Tor. Fingerprinting will kill you and you'll be obvious to a network adversary i.e. one of the few using Chrome, Chromium etc over the Tor network.