Standard alphanumeric LCDs based on Hitachi HD44780 controller never get old. These are still intensively used among hobbyists and pros. There are tons of software examples and libraries available on line. Anyway check out this shot tutorial where simple routine shows how to use custom characters on LCD.
Example is based on obsolete Atmega103 microcontroller but it easily can be adapted to any AVR. You’ll see that It is possible to draw simple pictures along text. Try it – its fun.