Processor speed and amount of RAM aren't important for the graphics.
I think that even graphics on the motherboard would suffice for this monitor. All you have to check: does it support the native (=maximum) resolution at the recommended refresh rate. That's rather easy to check, both for the sales person and for yourself.
I haven't purchased a new computer in quite a while. I'm looking to get an HP Pavillion. I don't game but I do some graphics work. Question is, I'm looking at going with a 22" LCD monitor, either Samsung or HP, what kind of processor speed, RAM and graphics card would you recommend to work with a new monitor that demands a higher resolution?