For a regular home user, the gateway IP should be the internal IP for your router/modem, which seems to be 192.168.0.1. If you have a router connected to another router, the IP should be that of the one you are connected to, not the one in the very front. You should not need to touch the subnet mask. It in a way determines how many usable IP addresses you can use. Having 255.255.255.0 gives you 254 available addresses and you most likely will not run out.
fenderman is right. If you have your modem on address 192.168.0.1, your DHCP server addresses should be under 192.168.0.xxx. Having the 192.168.1.xxx will put the addresses on a different subnet and the two will not be able to communicate with each other unless you have a router that will send traffic between each subnet.