I have exactly the same issue,
It seems very little support is available for cache by geoip in wordpress.
I would love to use W3 Total cache but it seems from what I read so far that SuperCache may well be better for your instance check under:
How do I make certain parts of the page stay dynamic? on the FAQ page
Not sure if a similar option exists for W3 Cache from what I read so far its seems that w3 cache lets you deselect a page from caching but thats about all.
Unfortunately for me, I want to be able to cache on a way more advanced level including a cache for mobile, language and country.
Something like this super cache with geo-ip targeting with some more options added would be perfect.
I'm still in my early stages of research into caching by Geoip but I read those options existed and thought it may be of help to you.