Your ISP did you a favor in talking you into using a router. There are so many things that could go wrong, and frustratingly so, in trying to share a single Internet connection without a router, that is simply is the easiest way to go. As you see, both of your computers get a non-routable, LAN-only IP address. This means that nobody from outside your LAN can get into your computers without your permission and cooperation-a real improvement on your security. It also indicates that you're only using a single IP from your ISP, which should mean you're spending less on your ISP bill.
Crossover cables are used ONLY when connecting a host to another host. In general, a host is a machine that acts like (and usually IS) a computer. Routers, on the other hand, are supposed to connect TO hosts, so we connect to them with straight-through cables. Newer Mac network cards have autosensing so it really doesn't matter, but since pre-made crossover cables are often REALLY expensive, it's best to stick with straight through cables.