Answer for Will a 350 Mbps router be faster than a 150 Mbps? My download speed is approx. 37 through Time Warner

The answer depends on the context of the network you are talking about. Obviously 350 is faster than 150, but that figure is usually measuring the theoretical maximum speed of the wireless network inside your house. It has nothing to do with the speed of your Internet connection. So if your current router is powerful enough to max out the speed of your Internet service, then a faster router will not help. However, if your current router is not keeping up (or it is malfunctioning), then a faster router might help.
The first question to ask is what speed should you be getting from your ISP. You say your download speed is approximately 37 Mbps. That’s good to know what you are measuring at, but what speed are you paying for? If it is 30, then 37 is excellent (obviously faster than what you are paying for). But if it is 60 or faster, then that’s not so good. That is the first step in determining if you should worry about a new router. Let me know what you should be getting and we can go from there.