Minecraft is a sandbox game from Mojang, written in Java.
Check for the latest Java. You can find your current version from the command prompt with "java -version"

Manually Download and install the right Java for your system. Be sure to run the installer as admin, watch out for a possible unannounced reboot.
Manually Download and install the JavaSE JDK.

Buildtools instructions to build Spigot and Bukkit
Eclipse is a Java IDE, popular for some reason
How to learn the Spigot API
Spigot plugin development