HDMI is a data transfer protocol standard, just like TCP/IP or USB. And it's a dumb consumer-level standard...its professional sibling is called SDI. And on the C300 you get both options, and Atomos makes a higher end Ninja they call the Samurai that just does SDI instead of HDMI. HDMI was for HDTV, which for legacy reasons uses 1080i60, sending half the lines 30 times per second, alternating with the other half (all interlaced together) also 30 times per second. There is nothing a camera or anything else can do to alter the protocol...that's how the machines have all agreed to talk, and because it's so dumb a standard, you can expect any HDMI monitor or whatever to understand it.
But we don't want to shoot 30p or 60i (both are offered on the C100 btw), for cinema the standard frame rate is 24p, which gives a nice familiar texture and blur to motion when captured at a shutter angle of 180 degrees (1/48th of a second or 1/50th on the 5D3 is close enough). So how does one send a 24fps signal over a 60i protocol? I forget the technical term (you can google all of this of course, and please do) but they essentially just repeat frames alternating 3 repeats and 2 repeats to match the timing difference of 30:24. And the receiver, to deinterlace that redundant 1080i60 stream to 24p (23.98 is the actual rate on the Ninja also due to legacy concerns with synchronization) must figure out the cadence of repeats and drop the appropriate redundancies, leaving a steady and even stream of progressive frames.
The Ninja has to do this empirically off a moving image being sent so it can see which images are repeats and which are new and drop the proper ones. HDMI can't communicate that information sadly, meaning the Ninja waits with record disabled until it gets enough contrasty motion to see what to do.
As for your growth plans, I understand dipping your toe in, but a lot of this only makes sense when you have the full professional rig in front of you and understood, and then you can learn to make do with less. Good luck with your exploration however you go about it.
