Yes...the router is the way to go and will save you some money in the long run. You could purchase another computer name/ip address from you cable company, but they charge around $5 a month for that. I recommend you get
THIS router, you should be able to get one for around $80. It is so simple to install that anyone with any experience at all can do it. Just use your computer name as the host name on the router, enable DHCP and change the name of your pc and you are set.