JtheGamer :
So I am in the process of making a tech review channel on youtube. I already have a good tripod with a video head, soft boxes, and a rode shotgun microphone. The only thing is I haven't found a good camera that can do great video for youtube. Here is what my thesis is...
Budget: from around 400 to $500
Features: Good low-light performance, maybe auto-focus, a external mic jack (obvious for my mic), good zoom, and a good interchangeable lens.
*Can shoot at least 1080p* *60fps can be a option*
*Can be a mirrorless or a DSLR*
I have to disagree with BlueFireZ. The FZ300 is the wrong camera. It has a small sensor, poor image and video quality compared to any larger sensor camera, particularly in low light. Also, the fz300 is not particularly fast in AF (also mentioned as a goal). And of course it is not inter-changeable lens camera (another goal).
What you need to pay closest attention to if you wish to get good low light performance is sensor size.
If however you want good zoom (and why in the world would you need that for a technical review site??), then you have options but the majority of them have so-so image and video quality and are not mirrorless or DSLR.
If you want good video AF you need to forget about DSLRs. Because while DSLRs have the better lenses and generally the best at still images (mostly as a result of lens selection, but also due to AF capabilities and sensor technology) but in video mode DSLRs do not AF fast.
I've used several dozen cameras over the years. I currently own and use quite a few. Ignoring the still image portion.
From least capable to most capable:
Samsung Note 3 (my phone) it is handy, Does most things well enough for most facebook users.
Canon SX50 HS (roughly equivalent to the fz300). It looks like a DSLR, has decent manual controls (important), good "zoom". In anything but perfect light the video quality starts to fade. Noise, less dynamic range and autofocus falls off. But still better than the phone. My Son loves to play with this camera.
Panasonic TZ30. Slightly better image quality than the SX50 but much smaller. Fits in pants pocket. Bought as a backup camera for vacations. I only use it in venues where DSLRs are not allowed (less than 100 photos and maybe 10 videos taken in the life of this camera).
Sony rx10. A bridge Camera like the fz300 and sx50 but with a much larger sensor. Much better video quality in low light. Both due to the larger sensor but also because it supports a much higher bit rate. Decent AF speed in video but not lightning fast. A big bonus is this camera is weather sealed and it has a very nice lens. The lens is wider angle than most at 24mm ( This is a very nice FOV for group shots) and it is f/2.8mm constant (lets in 4x as much light as a f/5.6 lens)
Panasonic GH3, This is a larger sensor than the rx10. It is a m4/3 mirrorless. The sensor size means less noise and better DR in low light. The difference is HUGE when you compare it to small sensor cameras and still pretty large even against expensive cameras like the rx10. It is a interchangable lens system camera. So you can pair it with f/1.4 lenses which take in 4x as much light as a f/2.8 on and allow for much better bokeh (smooth, blurry backgrounds helping the foreground object POP). AF speed is dependent on the lens used. With most lenses it will more or less match the rx10.
Nikon d750. A professional level camera. With a full-frame sensor. While you can AF in video, you should only use this type of camera if you want to manually focus in video.
I left out a few, but that is a representative spread of cameras.
If you don't need weather sealing and are willing to give up some video quality (lower bit rate) and accept a little lower low light quality (not constant f/2.8) then I think the best camera for you might be the Panasonic fz1000. It is available on budget for a price of ~$450 used (in like new condition) from amazon. This is the one I recommend for you.
If you want the slightly better rx10, it is 600 from amazon in the same condition. The trade off is that it is slightly slower to focus and does not have 4k video.
Both of these are only capable of around 29 minutes of recording per button push. I believe the fz1000 is much shorter in 4k video, but I don't recall for sure.
If you want even better there is the Panasonic gh3. It can match the bit rate of the rx10, but with the larger sensor and the ability to change to an even better lens it has the best capabilities. But once you add in the price of the lens it will be twice your budget.