The fact that your ISP gave you 2 IP addresses means that these are the only two publicly-routabale addresses you have available to you.
Unless you only have 2 computers in your network, you need to come up with IP addresses for the rest of your network from somewhere. That somewhere is called Network Address Translation or NAT. Essentially the way this works is that the public IP address assigned by your ISP is given to the external interface of your router/firewall. The rest of the computers on your network (to include the server as well as the internal interface of your router/firewall) are given private IP addresses (either in the 10.0.0.0 range or the 192.168.0.0 range). The private addresses are then translated to a public IP address by the NAT server (usually a router).
Make sure the private IP addresses belong to the same subnet (e.g. router internal interface - 192.168.1.1; server - 192.168.1.5; DHCP scope - 192.168.1.10-254). If you need further specifics on how to set up DNS for such an arrangement, let me know.