Welcome, In this case, we have various type of micro-controllers, such as Arduino ( AVR base), LPC17xx ( ARM series).Arduino series are cheap. due to they have boot-loader they are easier than others.For Arduino series you can see link below:
www.arduino.cc
It's important to take account that Arduino hardware are open-source and theyre sours code and libraries are available in full-access, i.e. LCD library is available in the link below:
https://www.arduino.cc/en/Reference/LiquidCrystal
Arduino Uno R3 is a good and cheap board. it's available in link below:
https://www.ebay.com/bhp/arduino-uno-r3
another board but smaller with Arduino Uno detail is Arduino nano or pro-mini, and they are available it blow links:
https://goo.gl/XxDQo3
https://goo.gl/K4C7ci
ARM series are reliable and they have been used in industrial projects.