In order for a standard focal length zoom from the main choices, I would go with the Panasonic 12-35 F2.8 or Olympus 12-40 F2.8, both of which are stellar - but pricey. Obviously the Panny lens has OIS, whereas the Olympus doesn't (but the Olympus is a fantastically sharp and contrasty lens at all apertures and FL's).
Secondly, I'd opt for the 14-140 II (latest version). It's light, small, and apparently has better IQ over the older and heavier F5.8 lens (although I've never owned that lens, but the new version optically is really rather good) and has a great equivalent range of 28-280mm. I've used this on all my M43 bodies (EM1, GH3 and GX7) and find it an excellent walkabout lens with the only downside being the relatively slow maximum aperture. Then again its no worse than most kit lenses. I also have the 14-42 II kit lens that came with the GX7, and whilst it's not bad, in my opinion it's no better than the 14-140 but gives up a lot of reach (however is a bit smaller and lighter - not that the 14-140 is heavy - it's featherweight !).
Lastly, don't forget Panasonic's new 12-32 collapsible Pancake zoom. This really is a feat of engineering and is only about as big in it's folded position as a 20mm F1.7 prime. It's tiny, but incorporates OIS, and is really very good. Just a tiny bit soft in the corners at 12mm (nothing to be too worried about), but sharpens up nicely by about 14-15mm. In the centre the image is razor sharp at all apertures and focal lengths and is a very contrasty lens. About the only downside (for some) is the lack of a manual focusing ring (it's by wire so has to have a Panasonic body to manual focus), and at 32mm (64mm equivalent) , it's a tad shorter on the long end that other standard lenses, although I'd be surprised if the difference between 64mm and 80mm is that great.
I have all the above lenses (except the Panny 12-35 F2.8) - yes I know I have too many, and I think you can't really go wrong with any of them.