Forge is a free, open-source modding API most of your favourite mods use!
This repository contains the updated 1.4.7 MinecraftForge toolchain to ForgeGradle 5. It works for developing as well as running mods.
The update was done with backwards compatibility in mind, so it can run your old worlds, too.
You can get the latest release here.
Download the installer, which will install Forge into your vanilla launcher environment, where you can then create a new profile using that version and play the game.
Download and extract the MDK into a new folder, then follow the instructions in its README