We're well past the days when you had to worry about storage and speed.
Most processors should cover all trading needs. Storage wise anything more than 100GB to be honest is more than enough, depends on if you watch high definition clips mainly or play games.
Unless you're going to be playing games just search dell, meshcomputers, pcspecialist, ebuyer (maybe not the best), comet etc.
An integrated graphics card will do for anything but multitasking and games. Even then you could buy the cheapest PC you could find and get a decent GPU for £60. However I'd still recommend buying a PC with a graphics card rather than intergrated (unless you're going for a laptop then there's not much choice).
If you're going to be buying a whole new kit, windows 7 will probably already be installed.
It's been a while since I've looked at the PC market, but generally multicore = great for multitasking, single core (super speed) = great for single applications. Also, I highly recommend google chrome!
There's a thread somewhere on this forum (I think it's called "best from the web") which contains hundreds of pages of software suggestions, from screen shot software, video software to free office packages.
Waffled a bit but hope that helps?
Phil