Which lenses for GH4, and other questions? (Low - medium budget)

Hey guys, I'm basically new to this camera environment and have quite a few questions, mostly pertaining to my lens choices. Old point and shoot camera was lost/stolen, so now I'm in the camera market. Did a couple days worth of research, and I'll be buying the Pana GH4 soon (waiting for the GH5 release and hoping for a GH4 price drop.). I've heard almost nothing but great things about it, with the negative being its performance lacking in low light.

I travel quite often, and my photos/video are usually close - mid range. I do take some longer range, zoom-in photos though, so I'd like to get a good zoom lens. My lens budget isn't really too high, so I'd like each lens to stay under $700, if possible. However, don't be afraid to suggest some higher end lenses if they're really great for the money, as I might be able to purchase them at some later date.

LENSES: Thus far, I'm only looking at native M43 and Nikon lenses. Is this fine?

I've got:

Metabones (It seems great and is also the reason why I'm looking only at native & Nikon lenses)

Nikon 35mm f/1.8  (should I get the UV filter?  Is it useful?)

Panasonic 45 - 150mm f/4.0-5.6  (the zoom lens I was thinking of)

Olympus 15mm f/8.0 Body Cap Lens  (it's pretty cheap and looks like fun to play with.)

I think I'm missing something in the 12 to 24 mm range?  I don't know.

Also, is there a good cheap Nikon -> M43 adapter I could get?  One that won't affect the image, like the Metabones does.

VIDEO:  What's a good video lens?  I'm probably going to get a Glidecam (I think there's a new devinsupertramp edition announced at NAB 2015?  Don't know too much about that.), if that matters.  Is the Nikon 35mm with Metabones good enough?

FILTERS:  I read that an ND filter isn't necessary for the GH4, but that a polarizing filter would be great for it.  Can I get a recommendation on a good one?  I saw prices ranging from like $20 to over $100, and am unsure what to get.

Also, can I mount a polarizing filter with the UV filter from the Nikon?  Or is it a one or the other kind of deal?

Thanks.  It's a lot of questions, I know, and hopefully I can get most, if not all, answered!