One of the best emulators that will find for free is "Google Chrome". Simply go to Tools - Developers Tools. Click on the small mobile icon present on the left side.

You can also open developers tools using Cmd + Shift + I or Ctrl + Shift + I.

Using this emulation tool, you can test your design for almost all types of mobile devices. It also has features like Network throttling that lets your see how your website loads in slower networks.

I hope this helps. :)

I use google chrome's emulator for initial development and then will test out in a few important and widely used actual devices, ipad, ipad mini, samsung phone for android and iphone later after the development and finally fix if there are any issues.

Use Geny motion as the emulator, which has very good features with wide range of devices, the best in Geny is u can connect a real device and learn the emulator all the sensor data and use can use the same later. Another option is Bluestacks.