Memory or ram is measured in Gigabyte and the more you have the better.
Downloading music etc is governed by your Internet connection, what laptop you have has no real effect except in terms of storage, which means a harddrive,which again is measured in gigabytes and again more is better.
Not sure what you mean by taking photos unless you mean an inbuilt web cam as your photos will obviously come from another source a digital camera or video camera perhaps.
What laptop to suggest also depends on what you will be doing on it. If it is just for surfing,email,office stuff and the like, your budget will get you a very fair laptop.If on the other hand you will want to do a bit of modern gaming then you will be toiling with your budget.
As for taking out an extended warranty,I personally belive they are an expensive waste of money. There is much help to be had in forums such as this and it is free.