My tips - don't bother with anything more than 1080p unless you have a 4k TV or want to make broadcast quality vids. I use 2.7k on the Mavic and render into 1080p. With the FZ300 I admit I do sometimes use the 4k option as there is no 2.7k one.
Remember the 180 degree rule - shutter speed twice frame rate if possible, or add motion blur in PP (you'll need something like Resolve full version or Adobe Premier pro). In the UK the frame rate is 25fps, so you'll want ND filters to reduce the shutter speed to 1/50 - assuming that you can manually set the shutter speed, which you might not be able to as some cameras just go full auto in video mode. The FZ300 does permit manual shutter setting, but the aperture range is limited. On the other hand a school play is unlikely to have even lighting and shooting from a distance with a static camera the 180 degree rule is not really important. If you do move around with the camera do so slowly and smoothly.
For me the most important consideration, sound. As Andy says you will need an external microphone. Rode (example
) are the industry leaders for home video, but any reasonably priced stereo condenser microphone that can be mounted either on the camera or preferably on an insulated bracket to minimise mechanical vibrations will do.
I use a completely separate recorder if the video is important - in my case a Zoom H1. Using a clapperboard app on your phone you can synchronise the sound easily, or just record on the camera too, sychronise by ear later and ditch the camera audio in PP.
Get a reasonable NLE - there is a free version of Resolve if you don't want to spend anything to begin with. Adobe Premier Elements is popular, as is Cyberlink Power Director (which is the one I tend to use the most - I don't have any Adobe software any more). The issue with Resolve is that it is a bit complex, even the cut down free version, but it's very good.
One of my friends takes a lot of video totally ignoring all of the above - he uses a high end action camera (not GoPro, can remember the make) and a hand held powered gimbal. It comes out pretty well. So really, if you have a high end phone getting a gimbal
for it will give you a world of video making options - gimbals for DSLRs are a small fortune!