If you're only connecting the one computer, I doubt you'd notice the difference between 100 meg and 1000 meg (gigabit) so don't spend a lot of extra money to get it, but if the cost difference is minimal go for it.
Read everything that comes with the Wireless Router. You should be able to find some networking help there for your particular situation, though don't count on it being in depth.
Basically you just need to get things hooked up to one another and powered on. Then Power Cycle the Cable Modem. All the Cable Modems I've encountered "marry themselves" to a specific hardware address and don't want to talk to anything else. Power Cycling it will cause it to marry to your router instead of your computer.
Once that's done, the easiest way to pick up your IP address is to reboot the router, then the computer once the router is back up. There are other ways, but I'm keeping it simple on purpose.
Learning networking was one of the best things I ever did. I encourage you to pursue it if you're at all interested beyond the basics it takes to get connected.
Good luck with it and have fun above all.