Looks fantastic, but I'm a little worried about buying an older card. Im not extremely rich, and I'd like a card that would work for most games for the next 2-3 years. Im currently using a GeForce 9500 Gt, so anything is better than that.
Your main issue will be, do you have a Power supply good enough to run a 480 ?
In your situation (coming from a 9500) any of the three will be a huge improvement.
The 7850 I would say has scope to improve through driver updates, this is usual for AMD cards for a good few months after launch. However AMD have just announced that they wont be releasing a driver every month any more, so how that will pan out for newer cards level of improvement is any ones guess. Just mentioned it so you have the info.
As I said before you are the one who really knows what will fit your needs best.
For what its worth I agree with your concerns about the 480. However its price point and performance make it difficult to dismiss too quickly.
Personally I prefer the 560Ti. (it fits my needs best) You would need one of the higher clocked third party cards to have 480 like performance though, a stock or close to stock clocked 560Ti wouldn't compete with either a 480 or a 7850.