Don't bother setting up gzip compression for images unless you are serving uncompressed image types.
All the common image types (png, gif, jpeg) are already compressed and you will not gain much at all (if anything) from recompressing with gzip. It will just take up more resources for users when their browser receives them.
As for cookies, I agree with Devin. Just don't set cookies on that domain and it will be a cookie free domain.
Edit to expand on my answer:
If the static content you speak of is html, js, and css, it would be better to create a handler in a server-side language to see if people have gzip enabled in their browser. Almost everyone should have it enabled, but some don't and you'd be cutting them out. You would have to keep a standard version of each file and then another version of it gzipped ".gz".
You could just enable mod_deflate on apache to compress certain types of files, but it would do on-the-fly compression every time the file is requested. That is a waste of CPU in my opinion, which is why I suggest you keep two copies of the static files like I suggested and use a server side language to determine which to send.