[alx]

hi I'm not sure about the cost of the router and adapters.
If you can run the cables you'll need two cables, a pci ethernet card and a router. this might be cheaper than wireless
If you go wireless you'll need one adapter for the laptop and another for the HP and a wireless router.
You can go to a computer store and they will tell you the prices on these components.
why don't you try to connect using the usb on the laptop and ethernet on the HP.

I have a 2wire modem and two computers networked. One is conected to the modem using USB and the other with an ethernet card. Yes the two computers can be online at the same time.