The Mongol Rally was founded thanks to a Fiat 126!
I'd recommend getting an air-cooled model, the later the better. I say this because there's far more spare parts available on the continent for the air-cooled, and local mechanics will be more familiar with the air-cooled engine. The 126 is to Poland what the Mini is to England I guess. And I recommend the later models not just because they'll be in-theory more reliable, but they have more refinements to the car itself that might make your journey more bearable.
I would not recommend that length of journey for 3 people, the guy in the back is going to get tired of being cramped... and that's even before you put luggage in the back with him.
Lina went from Essex to Slovakia and back a few years ago, you can see her trip updates
here. I think she had 4 breakdowns, but recovered from all of them and made it back in one piece!