How to make your own proxy server from a computer behind a router?

Question

linux

Actually, the question has already been asked, in the topic.
What is available: a computer with linux (any one can be installed), a d-link dir 320 router and a dedicated ip address from the provider.
First, the Internet enters the router, and only then it is distributed to cars and a wi-fi network.
Is it possible (and if so, how) to organize your own proxy server.
So that I can use it remotely, and at the same time the ip address of the remote machine does not change.
There are services where there is a binding by ip and you cannot add more than one.