You can do some of this just with ssh. It depends on your client, but the command line version goes as follows, and putty and other ssh clients have the facility to do this.
First approach is called dynamic port forwarding, and effectively turns your ssh session into a socks proxy.
On your local machine, do something like:
ssh -D8080 user@debianvpsip
In your browser, or any other socks proxy aware software, you can set the proxy server to be
127.0.0.1:8080, and any traffic sent to this port will go out to the internet as if originating from your vps.
The second approach, if you wanted to target a specific destination, you can use local port forwarding:
ssh -L1234:remoteip:80 user@debianvpsip
This creates a local port 127.0.0.1:1234 and any traffic sent to this port will be forwarded to remoteip:80
In both cases the traffic will appear to originate from your Debian VPS.