Good cheap router with easy port forwarding for Minecraft Server?

Tp-link seems to be good and some of them can easily have their firmware updated. Just be sure to dmz the router. Otherwise you will have a nightmare of a time port forwarding

Most of your questions are irrelevant. Any router you find will be compatible with Timewarner cable and have port forwarding capabilities, Easy port forwarding is another story. Though it is easy you might not find it so, I only say this because the question itself illustrates that your not to savvy when it comes to networking.
Here: http://www.amazon.com/...001UI4RTG/

This router is a netgear so it has a fairly common interface so help will be easy to find help. You will simply log into the router and enter the port forwarding section and enter the info.
That part may be tricky, but basically when entering port forwarding info what is important is you list the IP address of the device that needs the ports opened (The computer your playing on) and then the port number and whether its UDP ADP or both. (Both if your not sure). They will often have a name feild, this doesn't matter so enter whatever, its just for identification by people making the entry(you).