Actiontec MI424WR / Advantages To Gigabit Ethernet?

I am moving into an apartment thereafter. I have an HTPC in use, a personal computer for gaming/processing, and my fiancee has an Apple Macbook Pro that she uses quite often. I have an HDHomeRun Dual (2 tuners) for streaming OTA/QSM cable over the network (the HDHomeRun plugs into the network, not a computer). I also have a TV and Blu-Ray player that have ethernet ports.

Currently I use Verizon Fios and their Actiontec MI424WR router, which to my knowledge has gigabet ethernet. When I move I will probably be saddled with Comcast Xfinity Internet, which will supply a cable modem if I want, but no router. The only router I currently own is a Zyxel NBG-419N, which has only 100/10 ethernet ports. My current computers all have gigabit ethernet. For the home theatre components and my HTPC, I plan to pick up a network switch with gigabit ethernet. So my questions are:

1. If I use the Zyxel and the Comcast cable modem, would I be throttling my network speed at the router? I would hate to choke my speed just because one component does not have gigabit ethernet.

2. If I were to upgrade to, say, an Asus RT-N56U, would that make a huge difference on network browsing and throughput speeds?

3. Finally, what kind of cable is needed to maximize discernible speed increase? Cat5, Cat5e, or Cat6?