This can be accomplished fairly easily by making sure that your host will provide you a shell account on one of their machines. That means, you will be able to use a telnet client to run software, specifically Lynx, on their Unix machine. Even if you just want a simple counter, your best bet is to make sure they allow you access via a shell account. If you want to include CGI scripts, you will either need access to a cgi-bin directory, or your host will need to set up your server to allow CGI scripts in any directory. Ask any potential host if they allow that.
Server side includes are an easier way to accomplish most of the tasks CGI can accomplish.
If your host does not provide this capability, it's not the end of the world. At first, I didn't know that I wanted my own domain name. I ended up putting up with a lot of crap from my host because I didn't want to lose all those links and bookmarks. When I finally decided I had to move the site, I also decided not to let that ever happen again. It's easier to remember, it's more professional, and most important it is permanent.