the best lcds are based on the HD44780 chip. These are the most widely avaiable ones and avaiable from a variety of manafacturers. Check ebay, you should eb abelt o get them for under 10 bux.
These screens do have 16 pins in them (14 without a backlight).
TO reduce the umber of pins you use you can use libraries like the LCD4Bit (around 6 pins I think), or get a backpack that will take serial or I2C signals and write to the LCD. These backpacks use 2 to 3 data pins on your arduino.
Moderndevice.com has a serial backpack. I haven't used his, but I've used the chip and code his backpack is based on.