VPN means Virtual Private Network. It is a very generic name which covers any kind of technology aiming at emulating the security benefits of having "your own wires" while doing it over the wires which are already there.
A VPN can help for privacy issues only in a specific context: namely, whoever wants to spy on you controls a specific part of "the Internet" through which your packets must go; e.g. the envisioned enemy is the government of the country in which you live, and you assume that this government has complete control of the national telecommunications infrastructure. To thwart them, you establish a VPN between your home machine and an external system (outside of the reach of your enemy) to which you forward all your communications. The attacker will be able to know that you have some network activity with the World at large; he may even have a relatively precise notion of how much data you exchange. But he will not be able to discover what data you send and to whom (ultimately -- you send everything to the external system, which then forwards it to the intended recipient).
There are various technologies to implement such a VPN, and SSH tunneling is one of them. Therefore, you already have a VPN !
In such a setup, the external system is "trusted". This is the technical term which means that it is in the ideal position to backstab you. To avoid the potential problem of having a single trustee, you can cascade them:
- You encrypt data and send it to External System 1.
- ES1 decrypts the data, and discovers that the data is itself encrypted with another key, and is advertised destination is External System 2. ES1 forwards the data to ES2.
- ES2 decrypts the data, and obtains the actual plaintext data and destination.
So that's double-encryption (the plaintext and intended final destination -- the Web site you want to browse -- are first encrypted with ES2's public keys, and the result, along with ES2's name, is encrypted again with ES1's public key). This can be viewed as two VPN, one nested within the other. Your privacy is secure as long as either ES1 or ES2 remains honest; both would have to betray you in order to uncover your Web traffic.
Tor is a tool designed to do this double-VPN trick -- actually, with possibly more than two nested VPN, and with automatic randomization of the external systems to use. It is a good match with your expressed requirements (as I understand them).