Olympus OMD EM5 as first serious camera purchase?

You could do a lot worse. I love my OM-D. It's light and fast and has good image quality.

I believe that aside from the 12-50 kit lens, the only weather-sealed micro 4/3 lens is the new Panasonic 12-35. Which would put you over budget.

Personally, I really like the prime lenses available for this system: the Panasonic 20mm and (especially) 25mm, and the Olympus 45mm. Your mileage may vary.

I hope you have a great trip and take wonderful pictures.

--
Ben