If you're through a router, your IP or Mac address is already hidden to outsiders. Using a router, you have an external IP and as many internal IP's as you have ports, delegated by the router. Meaning, the internet can see your router's IP, but cant see your actual computer's internal IP address, and can't access it directly, except if you get a trojan or similar virus that broadcasts your internal IP from the inside out.
Using a router doesn't hide an IP or MAC address. your external IP is still avaliable. and most likely your mac address as most of them clone your nic when it's first hooked up. although what ever internal IP address your using like 192.168.0.6 will not be seen
If your after hiding your IP or Mac address from server logs etc.. you really need to use a proxy server. like on in Japan or China. and yes it is quite possible that using the proxy serve will decrease your speeds dramatically.