1) First of all, the term "router" is often used incorrectly. Some have no modem, and some have a modem. Just be sure you're getting the correct device as a router by itself is just for connecting LOCAL devices.
And a "1Gbps" router is referring to the ability to connect via ETHERNET locally to other devices. If it has an internal MODEM that's a different specification.
2) 20MBps or 20Mbps?
One is MegaBytes and one is Megabits, though I'll assume you mean Megabits. Generally speaking any MODEM can handle that.
3) So as said, it's probably your ISP provider that is limiting you. You need to find out what the DOWNLOAD speed of your plan is. Actually, you probably mean MegBytes/second because i get 1.3MBps in Ontario, Canada with Bell.
You probably need a FIBER NETWORK to get 20MBps in which case they'd provide you with the proper hardware. Not many places even offer bandwidth that high.