Whatever you do Ken, do not listen to Striker!!
Nah only kidding. I agree with him on the sheep (ah sorry RAM, i.e., physical memory), but disagree with needing a 3GHz CPU as a minimum. The CPU speed should be the least of your concerns (slower and/or older CPUs are heaps fast enough; all most modern CPUs do is sit there and do nothing because the rest of the system can't keep up). Also, ... even though laptops can do what desktops can, a laptop will cost 2-4 times more than a desktop of equal computing power.
Without needing a monitor & other peripherals you should be able to get a very slick and fast new system for under $500 and a very capable system for under $350 --- provided you already have the software you need or can get it for free. But you will need to find someone to set it up for you if you want the box to just work out of the box. (Geez that sounds aweful familiar or am i just repaetin moyself..??)