It’s best to show us what you are talking about. Anyhow, in general, set the logo to position: absolute and its container to position: relative. The z-index doesn’t matter, as long as it is higher than anything else, so probably 2 would do. But you may not want the logo covering anything else. Wow, 1024px height sounds too tall to me. Sounds lke the logo will cover your whole page.
Sorry, I was away for a while. I did look at the site before, and TBH, that images looked way too big. I’d suggest just a normal-sized logo up in the left corner.
When using position:absolute, that position must be in relation to something. Whatever parent element has a position (such as relative or absolute) with provide the positioning context. f there is no such element, then it is the viewport.
In a situation like this, though, having a huge image on the page like that will mean that it could cover everything on the page if set to a higher z-index than anything else, which would mean nothing else is clickable. I would suggest rethingking the design before going further than this, or at least post an image of what you are picturing. You could just set that logo as a background image to the whole page.