Even buying something off the shelf, that's not an absurdly expensive 'toy' (<$2k, certainly... so, not 'cheap' but certainly well within the 'hobby' range for a lot of folks). The camera is a few hundred more, but it's amazing how cheap HD-capable cameras have gotten recently.
If you build it yourself, you could put together a video platform like that for under $1k (including the gyro stabilized camera gimbal).
Hey JshWright, I recently got very interested in creating one of these and you seem to be pretty knowledgeable about this. Can you please give me advice on where a newbie can start with this? I would like to learn how to build one on my own from scratch.
The RCModelReviews youtube channel has a number of good videos on basic RC concepts (not multirotor specific, but the RC stuff still applies).
One tip I'll give you is to look into getting a Eurgle/FlySky/Imax/Turnigy 9x Transmitter (different brand names, same basic Chinese knockoff..). It's a solid radio with a lousy stock firmware, but there are a number of good open soruce firmwares out there that are very easy to flash onto the controller (especially if you use something like the SmartieParts programming board). For ~$100 (for the radio plus the programmer) you end up with something that rivals radios costing an order of magnitude more (or so I've heard... I've never touched a high end radio).
I'm approaching the hobby in stages:
1) Buy a Blade mQX (which comes with a cheap transmitter) and learn the basics of flying a multirotor
2) Get a 9x transmitter, mod it, and learn how it works
3) Get a 'JR compatible' OrangeRX DSM2/DSMX module for the 9x, so you can bind it with the mQX and get used to flying with the full size 'real' tranmsmitter
4) Get an 'ARF' (almost ready to fly) kit (this should include the frame, ESCs, motors, props, etc), and a flight control board (I'll probably start with something cheap like the Kk 2.0). This is a good time to learn things like "What is an ESC?".
5) Start modding your ARF quad (replace the ESCs, add a camera, get a more capable flight controller (like the Arducopter), etc)
I recommend checking out forums like RCGroups, there's loads of information there.
There are many ways to start into the hobby. You can get yourself a radio and a simulator and learn to fly on the computer first. You could go for an off-the-shelf solution like the DJI Phantom that will fly very well without much tuning or fiddling (but it'll cost the part). Or you can go the DIY way - a good keyword is "MultiWii", it's a fairly cheap but rather labor-intensive way of getting your first copter to the skies.
If you build it yourself, you could put together a video platform like that for under $1k (including the gyro stabilized camera gimbal).