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​I would definitely suggest shooting with a more "baked" in profile. Cine V would be good, also see if you can attach a ring light to your rig as that should help tremendously with any under exposed areas you might run into.
 
Shooing with F/2 lens and iso 1600 should give you great results, remember it is better to bump the iso in camera than to record an underexposed image. I definitely wouldn't shoot above iso 1600, but if shooting at 4k and down-resing your footage to 1080p - 720p  + using a noise reduction plugin you should get some pretty good results.

Thanks 
 

If you expose to the right (ETTR: http://www.eoshd.com/comments/topic/7922-ettr-the-ultimate-exposure-technique/ ) GH4 gives back really good images, even at 1600 ISO.
I also like the grain of the GH4, it is very filmlike. For the profile I would use Natural (with contrast, saturation and sharpness all the way down) or Cinelike D with just the saturation down, because it is very flat. I would not mess with master pedestal or shadows/highlight, you can see the problems here: http://noamkroll.com/the-best-gh4-settings-for-video-why-you-shouldnt-be-tweaking-things-too-much/
My 2 cents

Ive had to shoot a lot of things at 1600 and I have the best results if I shoot in 4k and downsize to 1080p. Natural profile, master pedestal: +5, -1 highlight and + 1 shadows, contrast -5, saturation -4, noise reduction -4, sharpness - 5, and use a lens that is f2.8 or less
I personally like the noise from the gh4 and downscaling definitely makes it look a whole lot better. sharpening will make the grain stand out more. In most situations where I know it will be pretty low light I use my c/y zeiss 50mm f1.7, which is sharp enough wide open to help with most extremely dark situations
I also have Neat Video but dont really use it that much unless its a shot that wasat 1600 ISO but is still like 2 stops under exposed. It may be better to just go higher in ISO to expose properly than to under-expose and try to lift in post (in terms of grain)
 

​Geoff hits on another good point.  He uses the Adobe suite in a PC environment, I use it on a mac.  (This is actually a really huge benefit in contrast to FCPX.)  I could send Geoff my assets and project files from a project we're working on together, and though we work on different systems - Mac/Windows, he can access everything and immediately start working in a Windows environment, without missing beat.  I've had to do this several times, and though I now it for granted, it's a wonderful "feature".

Personally I use Premiere due to it's photoshop/After Effects/Speedgrade intergration. I like the idea behind the method that FCPX uses, but I work on PC systems that I build myself, so it's not an option.

One thing I forgot to add is FCP X for all its greatness does not have curve for exposure. It only handles shadows, mids and highlights with 3 fixed points (I assume which means linearly). This looks really weird to me and I need to find some plugin because it's not enough. Anyone have any tips?

If your already decided, certainly act on it, but I actually migrated the other way. I started in FCP5 and loved it through 7. A fanboy for sure. When FCPX dropped, I was really excited. It looked slick and I was excited to try something different, but in end it didn't seem to work for me (granted, it has gotten better since). Since I already used and owned Adobe software (AfterEffects, Photoshop, Illustrator), I figured I'd give it a go and I haven't looked back.
I ended up really liking the way all the different programs effortlessly synced together, which made a profoundly positive difference in the speed and efficiency of my workflow. Additionally, Motion doesn't even hold a candle to AfterEffects. Even when I used FCP, I used AfterEffects, awful round-tripping and all.
All that said, they both are great tools and there's nothing that says you have to stick to just one. Aside from having a favorite, and we all do, any editor worth his salt should be able to work in the big three: AVID, FCP/X, Premiere Pro. (With a +1 for Davinci, who's really had some growth in the editor features department.) Good news is, they all have free versions/trials, so go play, my friend!
I'd be interested to see which you one/ones you end with, so keep us posted.  =]
 
*Oh, and welcome to the community!

I'd stick with fcx and substitute motion for after effects. 

Choose which you feel better, both are great tools; I'm a Adobe user but FCPX has been improving over the time and i really like the interface more than the Premiere Pro but I'm already used to Premiere.
In your case my recommendation it go for the FCPX because is a lot cheaper and at the end both make the task.
 

I like Premiere because it was obvious where everything was, even if it wasn't particularly efficient at anything. FCPX at first seems unintuitive because it's so different, but they save you a lot of time once you learn them. In terms of design FCPX looks like its going towards the future, whereas Premiere just wants to stay the same.
This philosophy trickles into the code base as well. Adobe refuses to rebuild Premiere, they just keep stacking code on code which creates tons of bugs.I found so many bugs with Premiere and corrupted projects that I just bought FCPX and never touched premiere again. Premiere ranks with some of the worst product experiences I've had, and the other two are Microsoft (Windows OS and Bing Ads).
 

+1 for FCPX, it is much faster in several cases, and i think it is really easy to learn 
Davinci Resolve Lite + Final Cut Pro X is far enough to make magic