What memory chip(s) should I buy to increase the memory on the computer to 4GB? What is the maximum?

Following those parameters your' maximum capacity should be 8GB however in many cases a computer with those specifications will support less than 8 GB. You would need to research that maximum memory capacity of your motherboard and from that point purchase memory sticks (RAM Sticks) that fit your PC (Either desktop sized or laptop sized) and make sure that the height of the memory sticks in millimeters will not contact with your' other components. Your' best bet for expand-ability is to acquire the maximum amount of memory that your motherboard supports in the fewest sticks possible.