You can build a great computer to suit from scratch. I agree with the multi-core CPU and would also look into getting a top-notch recording sound card. If you are planning on using it for gaming, movies, or just wish to have a great display you also want to look into getting a good graphics card. Nvidia and AMD come to mind.
The best CPU's out right now are the Intel Core i7's. There may be ones out there that claim they are faster but the i7's are proven for their speed in gaming. (I am an AMD fan myself but the i7's are much better as of now.)
Be sure to get plenty of power supply for your rig. The more fans you have, the more power you will need. Everything will need to go through your power supply. And, as mentioned above, cooling. I have had two computers die due to heat from intensive graphics needs while gaming. Water-cooled rigs are the rage but there is nothing that says they are superior to air-cooled.
Also make sure you have plenty of RAM.
If you are going to use multiple hard drives you may want to look into a solid state drive along with a "normal" drive. The solid state drives cost a little bit more and they don't carry as much memory as comparably priced disc drives but they are virtually instantaneous.
The best place to shop on-line is Newegg.com. Many of my fellow gamers have dealt with them with great results. DO NOT go to Best Buy. If you want to go to a shop go to Fry's. Newegg is the best for cost and service.