I know nothing about IPcop but here's my take:
Although a router may cost money, I think that would be the way to go. The router can do NAT translation and is very easily configurable with regards to VPN, ports, etc. Also, you may want to think about a wireless router since you mentioned that you have a laptop. Again, the router and any NIC card you may have to buy will cost money, but they are getting cheaper by the minute. Check out
slickdeals.net for, you guessed it, slick deals.