Welcome to the forum!
1. The price range can vary quite a bit depending on a lot of factors. If you're just looking to get into the hobby for as cheap as possible to see if you like it, I suggest you build a cheap tricopter. You could get something built for $200, including a transmitter and receiver.
Example:
http://www.instructables.com/id/Inexpensive-Wooden-Tri-copter/
You could also probably find a quadcopter build for around $200, but it will be a bit more since you'll need one more motor and ESC. Either way, if you're looking to do it for as cheap as possible, I suggest you copy someone's proven build. Don't try to pick out the cheapest parts on your own because you may end up buying a combination of parts that isn't ideal and your copter won't get off the ground. Then you'll have to spend more money fixing your mistake.
Tricopters, quadcopters, and other multi-rotors are similar, so what you learn, you can apply to building the others. Tricopters do have a servo on the tail to change directions, but everything else is essentially the same. Quads and others with more rotors are more stable and probably better for filming in most cases.
2. It doesn't require a lot of skill at all, especially if you're copying someone else's build (there are a lot of people who post build logs to help others learn how to build a copter). Things can get pretty advanced if you want to start picking motors, escs, batteries, etc. on your own. Also, as you start adding FPV, GPS, and other addons, it can get complicated. You'll also need to solder in most cases, but you may also be able to find plug n' play components. They seem to come out with new stuff pretty much every day.
3. When setup and calibrated properly, multi-rotors are very stable and easy to fly. I think the hardest part is getting over nerves when you have all your hard work and money up in the air for the first time! Also, a lot of mistakes or defective parts tend to cause it seem impossible to fly sometimes. When everything is working like it's supposed to, flying is easy.
