With that budget, I'd definitely look at either the Panasonic GH3 or the Panasonic G7. If you plan on using those 800$ on other gear besides the camera, then I'd say a used GH2 is the way to go, which you can find relatively easily for less than 300$.
Did you get the G7 with the 14-42mm f/3.5-5.6? It's a great starting point for a well-rounded kit. The aperture is terrible (f/4.1 at 18mm, f/5.3 at 25mm, f/5.5 at 35mm), but it is definitely a good (and very cheap) place to start. Obviously, the 12-35mm f/2.8 is much much better, but also much much pricier.
Guy talked about getting a 50mm lens. Well, that depends... If you get a 14-42mm, you can try for yourself to find out which focal lengths you like best, and buy a good prime lens accordingly. Just keep in mind that a 50mm lens on the G7 is equivalent to around 115mm in UHD mode. But I do agree with going the Nikon route, as their lenses work great with speedboosters, if you plan to go that way. One thing, though: give preference to full-frame lenses! You never know if you won't buy a full-frame camera down the road, and they'll work fine on any sensor size, even with speedboosters.
When you speak of metabones adapters, do you mean the passive ones or the speedboosters (the speedboosters give you wider angle of view and increase exposure by 1 stop)? Either way, there are cheaper options. Any brand of passive adapter will do the job, just be careful with the cheap ones, as they might be poorly made. I use a 25$ Nikon to m4/3 adapter, and it's built like a tank, so as long as you keep away from the 5$ ones, you should be fine (as long as you're not planning on putting huge telephoto lenses on them without any support).
In regards to the speedbooster adapters, Mitakon makes a 200$ Nikon to m4/3 speedbooster that's almost as good as the Metabones, and much cheaper.
One last thing: as a micro 4/3 user myself, I have to recommend you look into C-mount lenses. They're super cheap, and super fun. Most of them are useless for professional work (too soft, way too much chromatic aberration, weird colors and weird flares, etc.), but they always produce a very unique look. The Fujian 25mm f/1.4 is very easy to find for less than 30$, and if you look it up on youtube you will see how cool it is. But if you're looking for lenses for professional work, yeah, it's no good.
Guy is absolutely right in every thing he said. Just thought I'd add one other thing that might be of importance to you: the GH3 has an audio output jack, so you can monitor what you're recording with some headphones. The G7 doesn't, which may or may not matter, depending on what kind of audio gear you're planning on using.
Great article, and great thinking by the filmmaker. This is definitely the kind of post we need as often as we can here at No Film School! I appreciate it very much it. And Jake Roberts' story sure was needing a sequel after Beyond the Mat.
With a budget of 700$ I'd definitively look into the G7, which sells at around 600$ with a nice 14-42mm f/3.5-5.6 lens. I own one myself, and I think it's the absolute best beginner camera out there right now that will be around for a while, along with the newly released Sony a6300 (if it's as good as it reads in the specs) and which should sell for around 1000$.
The G7 is pretty much as good as the GH4 in all video and still features (sharp UHD, very good battery life, light and small, not great in low light, around 10 stops dynamic range, etc.) with a couple of features missing:
-no true 4K (4096x2160. UHD is 3840x2160);
-no headphone jack;
-no V-log (which adds around 2 stops of dynamic range);
-slow-mo tops at 28mbps 60p, which is not all that good if you want to grade your footage heavily;
-30min. recording time limit;
-no 10-bit output via HDMI.
There are some other differences, but these are the ones that matter for video shooters.
Then again, if you're only looking for a camera specifically for shorts, maybe the Blackmagic Pocket Cinema Camera would be a more suitable option, as it has very good dynamic range (around 12-ish stops) and records RAW or ProRes internally. Then again, it brings many costs that the G7 doesn't, as you'd need to invest much more in storage and battery solutions.
If the 700$ budget you mention is not only for the camera, but also for some other gear, then Guy's suggestions are probably the way to go.
I think it's very good. The sound needs work in the mix and in the cuts, but that's been covered by the comments above. Besides that (and the "Portrit" thing), the only one thing I thought could be better was that the shot starting at 1:02 ignores the subject of the documentary. It's a good looking shot, but it just goes by the photographer and doesn't care about him. To me, it felt like it was a shot trying to draw attention to itself, instead of drawing attention to its subject - which is fine in some cases, but here I felt it was out of place.
But that's a little thing, and maybe it was just me who felt this way. Otherwise, very good job!