Add a WAP works.
Replace router with wireless router works.
So take your pick. Many choose to replace the simple router with the wireless router because purchasing the matching brand of WAP sometimes is more expensive. Also, replacing the router does have some other advantages--one device instead of two, you don't have to run a cable between the old router and the new WAP, and you don't lose one router port to connect the WAP.
Some add a less expensive wireless router to the existing router. The wireless router functions as a WAP when it's DHCP server is turned off (leave the DHCP server on the old router turned on). Check the wireless router to see if it can be configured to function as a WAP before you purchase.
I have what I hope is a basic question. My current home network consists of two computers wired through my router to my cable modem. I'm going to be getting a laptop with a wireless card. Can I just buy a wireless access point and connect it to my current router or do I need to buy a wireless router that supports both my hardwired computers and the future wireless one? Is the price between an access point and a wireless router negligible?