Most contemporary switches are auto MDI/MDX, meaning they detect how the cable is wired and adjust accordingly. So, it really would make no difference. Typically however though you would use a X-over from workstation to workstation. Straight through when connecting workstation to switch or hub. In your case, the switch would be the LAN ports on your routing device.
As far as issues, if you can use a X-over from your computer to the router's LAN side then it's auto detecting and there are no issues to have. It will either work or it will not.