The DJI Phantom is pretty much the standard in consumer-grade multirotors. It's plug & play, sold as a complete package with transmitter included, and for what you get it's actually not that expensive. If you're reluctant to fly a $500-$1000 UAV, get a cheap multirotor first and learn to fly. The Hubsan X4 is under $50, for instance.
If you're a tinkerer you can build your own for a lot less, but be prepared for a LOT of fiddling to get it right (and the crashes that come with the fiddling). I fly a DIY F330 (same dimensions as the Phantom, only 'naked' frame) with an Arduino-based flight controller (APM2.6). It has some advantages over the DJI system, such as unlimited waypoints for autonomous flight. It can carry a gopro, and replacement parts/batteries are a lot cheaper if you get them from China. I don't get anywhere near the battery duration of the DJI, though.
So: if you're looking for a new hobby: build your own. If you just want to fly: get the DJI.
Couldn't agree more. I had a Parrot 1.0 and it was of low overall quality. I have a Phantom (v1.1) and it's fantastic; a friend just bought the v2 which is even greater.
Among the differences: the Phantom has an actual radio, with ranges of over 500m (it would be very surprising if Wifi covered the advertised 300m of this new Parrot); you can change cameras as you wish (or, after a crash), it can fly really high and really fast, etc.
You can get a Phantom 1 for under $350 these days (without a gimbal), or a 2+ (camera and gimbal included) for around $1000. I would recommend buying the 2 without gimbal ($550) and the Zenmuse gimbal ($150-$200) -- and if you already have a GoPro you're all set.
Alternatively, you can buy a Hubsan H107D FPV which comes with a radio with a screen, for under $150! I don't own that one, but I have the Hubsan X4 which is a lot of fun (and completely safe to fly indoors).
If it is possible, you would be severely limited by the WiFi signal radius. I'd highly recommmend a normal 2.4 Ghz TX since they're designed for this stuff. The phantom comes with TX, but if you go the DIY route I can really recommend the Turnigy 9X from HobbyKing. It's only $60, has 9 channels, comes with receiver and people won't laugh at you because you're holding an iPad or a toy-like transmitter.
For learning how to fly in the sub $100 price range, get a Hubsan X4 H107C - don't be put off by the low price - they are crazy fun to fly. For the $1000+ price range, the DJI Phantoms are great. For the $500 price range, check out http://www.thepocketdrone.com - the most successful drone Kickstarter campaign of all time (raised almost one million dollars). Disclosure: I work for AirDroids who manufacture the Pocket Drone.
Before you even start, have a look. You'll need a frame kit, motors, ESC and a flight controller as well as a transmitter and a reciever. You might also want an FPV kit so you can see where your flying and a GoPro so that you can film what you see.
Have a look at the DJIF450 or DJIF550 frame kits, start with one of those cost me around £400GBP, you'll learn more with one of those than a Phantom and you'll be able to replace parts easier.
If you're a tinkerer you can build your own for a lot less, but be prepared for a LOT of fiddling to get it right (and the crashes that come with the fiddling). I fly a DIY F330 (same dimensions as the Phantom, only 'naked' frame) with an Arduino-based flight controller (APM2.6). It has some advantages over the DJI system, such as unlimited waypoints for autonomous flight. It can carry a gopro, and replacement parts/batteries are a lot cheaper if you get them from China. I don't get anywhere near the battery duration of the DJI, though. So: if you're looking for a new hobby: build your own. If you just want to fly: get the DJI.