My instinct says I should go with Cmd+K, as it's standard in so many apps nowadays and doesn't hijack the default Cmd+F. I've also seen Cmd+/ and other things being used elsewhere.
Do you have a preference or do you feel like there's a de facto standard emerging here?
The right one would be:
Do you even need some key combo to go to the site search box?
How many times a day do you really do that?
If you really-really use this, which key combo do you use or would prefere to use?"
(yes, I'm tired of absolutely useless search on the most of the websites which sometimes doesn't implement even a full-text search on the topic contents AND ALSO is stealing my keys and focus)
2) I feel like overriding default operating systems patterns is almost always the wrong move for any question. I'd get a bit ticked if CMD+F worked differently than I expect for finding an item on a page.
Edit:
* Github supports /
* Google supports /
* AWS Console supports Alt+S