As Devrij says, it depends what you mean by multi-tasking. If you mean a few things open at once then any modern CPU will be fine, no need to go anywhere near the level Doomedspeed suggested.Most ordinary tasks don't require very much single threaded performance at all, even if they are poorly threaded, so a cheap AMD (6300 or 8320 )is fine, or possibly an i3. Higher than that sounds like a waste of money to me.
You'll need some RAM (all computers do!) - multi-tasking generally means you need more of this as each task will use some, but again it depends what you would be doing with those tasks. I'd suggest perhaps 8GB RAM as a sensible place to start unless you're doing something abnormally RAM intensive (give us some use examples and we can help!)
To stream TV you may need a TV card (e.g. an HD arial running to your computer would need a TV card to let you watch it) - I'd look to get quite a good one as cheap ones really ruin the experience. Of course, if you're e.g. streaming video from the internet then this bit is totally unnecessary!
Multi-screening doesn't require multiple GPUs, one can drive several screens. As Doomedspeed mentions, you don't need a discrete GPU at all, though a lowish end one is probably a good idea, again depending what you actually do with the machine. Also, this depends what you chose in the CPU section, as some CPUs come with onboard graphics and others don't. If you get an Intel celeron, i3, i5, i7 or any AMD APU then it'll come with onboard graphics of varying capability. If you get an AMD 63xx, 83xx, Intel Xeon then you won't. Once you've chosen a CPU we can advise you better
The things you've specifically mentioned don't really need lots of GPU power (again, multi-tasking being so vague I'm just ignoring it).
