Not a good idea to run both server and client on the same computer, just going to say that right off the bat. That said, a good processor (such as a i7/i5) is advised. at least 8 gigabytes of RAM, and a decent GPU(for the client) as well. Number of cores do NOT matter unless you plan to do many things at once on the computer. If you insist on running both client and server on the computer, I suggest at least a 4 core, since you need 2 cores each for server and client for optimal performance. You also need a decent upload and download speed, as well as a good ping.
As far as processor goes. it's the gigahertz that matters. 1-2 gigahertz will probably not be enough.Closer to 3 or 4
But again, I suggest having separate computers for both, especially for a big pack like Monster. I have seen many many threads about people who attempt this with even beasty computers, and run into serious lag as soon as someone logs onto the server from the server computer.