1) Q: "What AMD processor would you choose for me, and why?"
A: None. Reason being at every pricepoint, low-end ($100+), mid-end ($200+), and high-end ($300+) Intel has the best performance. I don't care what people say about "Oh AMD has cheaper quad cores." A dual-core with hyperthreading i3 will beat an AMD quad any day of the week.
2) I would suggest either the i3-3225 or the i5-3570, depending on your price range. The i3-3225 is one of the new Ivy Bridge i3's (2 cores/4 threads) with Intel HD 4000 graphics (relevant to you if you don't buy a graphics card) at around the $120 price point. For that price range, it doesn't get any better/faster than this. The i5-3570 (4 cores/4 threads) is at around the $200 price point and is the fastest Ivy Bridge quad (aside from the 3570k which can be overclocked to higher, but you don't need to worry about that). From a bang for your buck perspective this is one of the, if not THE best CPU on the market right now. It's super fast.
Overall I would really suggest picking up an Ivy Bridge i5 of any kind. Maybe a Sandy Bridge if you will save much money going that way. I don't know if any of the applications you will be using actually require a powerful graphics card, but if they don't the integrated Intel HD4000 on the one's I suggested will serve you well. If you do need a discrete card, and won't be gaming, something low-end like a Radeon 7770 will probably be fine for you. Good luck!
1: a6-3650 why? it will get the job done, comes with a decent graphics card, and is only $85.
2: i3-2105 or i3 3225. why? they get the job done. 2105 copmes with hd3000 graphics and the 3225 comes with hd4000 both of which are not quite as good as the a6's for gaming. all for ~$140
3: they all will run what you want its just a matter of how long they take to finish the workload. And the i3 will almost always finish first. http://www.anandtech.com/bench/Product/403?vs=289 (note i3-2100 is lsower than the ones recommended here but its enough to give you an idea)
The best quad core for the money is, i5 3570k for overclocking and the i5 3550 for not overclocking, but if your just going to go online and use youtube and itunes, a pentium will do and if you get one you can upgrade to a i5 3570k as they have the same socket.