You would want to use a wireless n access point (WAP) or set up a wireless n router as a access point.
As far as speed goes it depends on what speed you are referring to, LAN or WAN.
Here is how it works,
A router connects two separate networks and manages the traffic between them.
In most home network applications the router connects your local group of computers and devices known as the LAN with the Internet, commonly called the WAN or Wide Area Network.
Your WAN speed is determined by your ISP and is measured in Mbps (Millions of bits per second).
For example if you pay for a 3 Mbps Internet connection, you will get 3 Mbps.
No router or connection settings will change your 3 Mbps Internet speed. This connection bandwidth is shared by your entire LAN via your router. In a shared setting with several users this can be a big problem.
For example if you have a 3 Mbps Internet connection and one user is utilizing 2.5 Mbps of the bandwidth to stream a Netflix movie that only leaves 0.5 Mbps for all of the rest of the users on the LAN.
The only real way to speed up your Internet connection is to get a faster ISP or speed tier.
Now you can speed up the LAN connections between the local devices connected to your network. In your scenario if you connect a wireless n router configured as a wireless access point to your existing cable gateway then,
Your Internet connection speed will still be determined by the speed of your ISP plan.
LAN connections can be increased to Gigabit Ethernet or Wireless n speeds. The connection speed will auto-negotiate to the speed of the slowest device for either Ethernet or wireless devices.
What this means is in order to achieve Gigabit LAN speeds, all devices in the connection need to be Gigabit. This would include the LAN ports on the new router, the network interface cards in both devices and the cables connecting them. (CAT6)
Good Luck...