First of all, a big +1 to everything Scab Pickens said.
A good deal depends on how big and what type projects you are running, but here are minimum specs that I would recommend in any case.
RAM: at least 6GB for general purposes. If you are running several sample based VSTi's it may be a good idea to start out with more, though most computers have extra RAM slots which will allow you to substantially expand your setup. Running 64 bit will allow you to access a lot more than a 32 bit system-I can testify!! Good thing that 32 bit systems are almost impossible to find these days.
HD: at least 7200 RPM (SSD recommended). Again this will depend on if you plan on streaming sample libraries. I know Seagate has a nice SSD-HDD hybrid unit for a very affordable price. The performance is a little under that of a legit SSD, but the price is way better.
Processor: at least an i5
OS: Win7 or Win8. If possible I would go with Windows 7, as the compatibility in general seems a little rough in some areas of Windows 8 for some reason.
There is some good info on the Steinberg site's knowledgebase, in the DAW Components article. You will also find this in the forum Knowledgebase in my signature.
Asus R500A-RS52, Windows 8, 2.6gHz i5 -3230M, 6GB RAM,
Cubase Artist 7.0.6, Wavelab Elements 7, Focusrite Scarlett 8i6, The Grand 3, Melodyne Essential, Superior Drummer, EZDrummer and Pop! EZX, Samson CO1, Yamaha P-35, Mackie MR5mk2 monitors, and more....My tunes on: Soundcloud