The faster the CPU speed (that you can afford) the better. At least 2GB of RAM..more's better. Of course..high-speed (fast as you can get it) internet connection. A good video card helps graphics draw quickly and text is rendered a bit better than on-board video.
It's a good idea to get a motherboard that can support Sata at 6 Gb/s. As Seagate has mentioned, solid state drives aren't going to be a permanent solution for many years to come as there isn't enough NAND flash memory on the market for all the devices that aren't coming out.
A computer to browse the internet shouldn't need a dedicated graphics card and could use limited ram. I'd get a good CPU for multiple app use first, and then a solid motherboard and a hefty hard drive and maybe a smaller SSD for booting .