I suppose you could not worry about the 2nd display for now and add in a card later if necessary, but it helps to plan that out a bit.
If you're not storing movies and tons of big files a 120GB-128GB type hard drive should do. If you click on My Computer it should tell you how much space you're currently using up. Windows + a normal compliment of light programs will usually go about 30GB, plus pictures and mp3s. I can't guess at what you have but if the primary purpose is poker and you don't load it up with video and big games even an 80GB-90GB might work fine.
I looked up microdirect in the UK and as far as processors, it's £93 for the lowest end of what you'd want, £189 for the highest end + another £18 to get the fan you'd need to overclock it. I think there is a pretty good value or two in between at £156 and £166 which are effectively pretty close to the high end. That's with VAT.
Long story short, just doing a real quick sample build you get a pretty solid PC for £500, though you'd need to factor in the cost of Windows too (£72, or use Windows 8 preview frree until Jan 15th). Anyway one of the best new CPUs, a lot of RAM, and a very fast SSD. If you want to play games you'd need to add a video card, if you want Blu-Ray that's extra, etc.
You'd want to refine that and shop around for deals and alternate parts, this is just to give you an idea of where you're at. The core components here are really more than you "need" but if you're not looking to go for the bare minimum this seems to work for your budget range. As far as processing power thats as much as anybody really needs today.